Welcome back to Moscone West in San Francisco. You're watching theCUBE's continuous coverage of RSA 2023. This conference is back in a big way. Many thousands of exhibitors. It's got to be 50,000, 60,000 people here in a day two. Really, things actually kicked off on Saturday. Tonight is the big crescendo. A lot of parties going on tonight, tomorrow night. You know, we'll be going all day through Wednesday. Rotem Eram is here. He's the CEO and co-founder of Atbay. We're going to talk about cyber and the insurance industry coming together. Rotem, good to see you. Thanks for coming on the team. Yeah, thanks for having me. You're welcome. So tell us about Atbay. Are you an insurance company or a cyber security company? Well, we're both. Yes, yes, okay. Yes, Atbay is, we are a cyber insurance and security company using cybersecurity expertise. We've built an insurance company from scratch to provide insurance coverage for businesses, small businesses, medium-sized businesses in the U.S. We have more than 30,000 customers by now in the country. And we use our expertise not only to help them with their insurance, we actually step in and provide them with security technology and operations to help them avoid a claim in the first place.  We hear about culture and big organizations. Small business, they don't wake up in the morning thinking about security. They're trying to stay alive, that you're worried about cash flow, where they're going to get their next loan, how they're going to meet payroll, you know, how they're going to grow, whatever. They have a variety of challenges that they're dealing with. You know, security is not top of mind. So I presume security doesn't work that well in small business. What's your perspective? It doesn't, and you know, what we're asking small businesses is really unfair.  And after the crash, you realized that there was a critical vulnerability in the brake system. You needed to read the blog.  The manufacturer of the brakes takes no responsibility. They're not going to let you know. They're not going to recall the product. They're not liable. And you have 50 different vendors in your car. Each one breaks three times a year. Now you need to have a full-time mechanic. The amount of expertise and the cost to keep your technology stack secure is more than what a small business can handle. And then on the other side, it's not like you're dealing with your neighborhood criminal. You're dealing with nation-states, organized criminal groups from and every 15-year-old on the planet with an internet access. And so it's not a surprise that they're overwhelmed and they are underserved by security because they have no buyer. They have no budget. And even if you gave them the security for free, they have no operator. It's like if I gifted you an airplane but you have no pilot license, you won't be able to use it. And so even though we've been doing this for 20, 25 years now, we're not making any progress. The gap isn't getting close, not even close to that. I want to ask you about some misconceptions that I hear from small business owners. Yeah, we're not a target. You hear that all the time. Or all our data's in the cloud. Right, they're taking care of my security. Easy question, but explain why that... First of all, why is that... I presume you hear that as well. Why is that prevalent? And why is that not the right way to think about it? So what I would say is that small businesses are correct that they are not targeted. But what they are is it's a different kind of targeting. It's more like a drive-by shooting. Basically, with a small business, the attacker cannot afford to spend a lot of time. And so what they do is they cherry pick. And so they scan every IP address in America and they look for predictable vulnerabilities that can be exploited relatively easily for a quick gain. And so that's why we see ransomware or phishing as the two most prevalent types of attacks. So yeah, you're not targeted, but everybody is targeted by those kind of sweeping, broad scans. What you don't want to be is you don't want to show up on their shortlist. As somebody that has this flashing light, that big vulnerability that can be exploited. To your second question on cloud, what I will say is that cloud's not perfect, but from what we see from our data from analyzing the claims of our own insurers, we see that companies that are digitally native, that are cloud-first, are dramatically more secure than companies that still manage their systems themselves. And the reason is that small companies fail at managing their own systems. And so even though Google or Amazon or Microsoft are not perfect, they're better at managing your stack than you might be managing your own stack. There's a but, though, because you still have a shared responsibility piece that you got to secure the S3 bucket, maybe not the physical bucket, but you got to make sure that you're not putting sensitive data in there, that your developers aren't putting hard-coded secrets. 100%, but I can tell you out of more than 30,000 customers and thousands of claims a year, I think we might have had one that had an S3 Amazon bucket involved in it. Everything else is- Your customers, yes. Okay, is that because of you? We definitely help, but what I will say is that I think there's, look, being here in San Francisco, in the hub of high tech, we often tend to spend more time talking about problems that tech companies have, and we take for granted the level of sophistication that companies in San Francisco have. But everybody east of Reno has a different technology stack that is 10 or 20 years old, that is still on-premise. It's not cloud-based, and the way that they get attacked is to be honest, it's kind of basic and predictable, but not anywhere close to being figured out. Explain how your model works in terms of insurance and cybersecurity practices, and so how do they go together and maybe give our audience an understanding of that? Yeah, so security's been around for 25 years. Cyber insurance is a little bit newer as an industry, but it has grown dramatically, and insurance policies pay for damages from cyber attack, whether it's data privacy issues or restoration of networks or data, or whether it's even dealing with a ransomware incident. It includes first-party damages and third-party damages to your partners or lawsuits from third parties. But what we see is that in the most small companies end up, they can't buy security for all the reasons I mentioned earlier, and then they buy an insurance policy, they have a claim and the insurance policy pays for damage that security could have solved. And so we're seeing this two separate solutions that by themselves don't really move the needle in terms of fixing this kind of broken system, and what our approach as a new entrant into insurance, we're a cybersecurity company first, but we've built an insurance company with the idea that we would step in and we would help companies solve their security gaps, we would avoid the claim altogether, and so we would need to pay less for the claims, we could charge in less on the insurance, and everybody wins. And you'd be more profitable in the long run. So, versus an insurance-only company, might say, either I'm not going to insure you or you have to show me that you have a relationship where you've got adequate cyber controls, which a lot of small businesses don't. How do you help the company? Do you come in and do an assessment?  Great question, so what we do is, first thing that is really trying to understand what are we dealing with? Which assets do you even have, and what is the status? Is there anything here that needs immediate attention before we can even provide you with an insurance policy? We do that ahead of partnering with our security team. We run tests from the outside in, similarly what an attacker would do. So, if the attacker's doing a drive-by scanning of every business in America, we do the exact same thing, and we want to see, would you pop up on an attacker's short list for companies they should go after first? If we feel that the risk profile makes sense, and we help companies get there, we then provide them with a security exposure manager solution, management solution, which is basically a vulnerability management tool that brings in information from the outside, trade intelligence, information from inside, existing security controls that the company already has. We run it through our own risk engine, so we run it against our own claims data to try and understand which one of these things matters, because we know companies, there's always something that needs fixing, so we want to make sure companies spend time only on the things that actually drive claims and drive incidents, and then we have our own security team that manages in some sort of a virtual kind of sock, virtual CISO relationship, where throughout the year and during these issues, we help them remediate whatever needs help. If they do have a claim, our own response and recovery team would come in on the scene and actually restore the systems and help companies get back to... This is interesting, so you make sure there's no, well, you look for open wounds and sort of identify them, and then are you a managed service? Is that right? There's a very strong managed service component here. We don't replace the MSP in terms of taking care of basic IT needs, but we definitely up-level the security team in terms of giving them that kind of depth of expertise, and also the 24-7 monitoring that we can afford to do, and they can't. So it's interesting because you mentioned IT teams. A lot of SMBs who are running mostly in the cloud, you don't have an IT team, right? So what do you do in that instance? Do you partner with sort of IT teams, managed IT service providers? Yes, 100%. So we find that about a third of our customers don't have any IT person in the company. By the way, not only those that are on the cloud, even those that are on-premise, many of them use Mike's computer shop from down the street to manage their security for them. Then we partner with Mike and his peers and we help them, we give them our tools, our services, our expertise, and we work with them to help the customer. And you act as a fractional CISO, is that right? There's, yes. I would say that's a good way of saying it. Is that a fair way? Yeah, okay. And I think what matters here is that once we're on, once we sold you a policy, we tend to probably lose more money than you. And that gives us a really big incentive to help solve an open issue. And so we would deploy our own resources and use our own scale and our own expertise to make sure that we get the customer back on their feet. We are much happier spending money on improving security than paying claims or paying the attackers. Well, what's interesting is you've got a, at least a quasi-vertically integrated stack, if you will, between insurance and cyber.  And if, for whatever reason, something goes wrong, you're there to help fix it. You're taking responsibility for that. There's not that kind of finger pointing. And what I will say more, there's a real opportunity here to unlock savings. Because again, once we're your insurance provider, it makes sense for us to pay for the security controls that would improve your position. What we find oftentimes is that for us to subsidize, fully subsidize the cost of a security control would reduce our expected losses. And so we make money by giving you security. And we just feel that there's a magic here that happens when you combine the incentives and scale of an insurance company with the fact that smaller businesses, they can't really afford to buy these controls on their own. They don't have anybody who knows that they should even buy those controls. And look, if you take a step back a little bit, and when we're in the echo chamber of cybersecurity, it's hard to see kind of the bigger picture, but insurance has always been the one to standardize the risk stack. I mean, the reason why right here on this ceiling, there are sprinkler systems. It's not because whoever built this building is passionate about the brand of the specific sprinkler provider, or that the technology, there's a code in the building. It was created by the insurance company. Insurance companies provide the standards. They provide the not only kind of the trade-offs in the decisions you make and the incentive to improve your security, they also help standardize the ecosystem and say what should you get, what shouldn't you get, how much should you pay, how much is an EDR worth? You know, who can, what is the right price for an EDR? Insurance companies can tell you that because we see 25% of our book has EDR, the other 75% doesn't. I can tell you what is the average expected loss for each bucket, and that's how much you should pay. Okay, and you're in the business of reducing the expected loss. I mean, obviously, talk about the changing risk profile. I'm really interested in this.  Now you got AI coming in, and not that you didn't have it before, but now in the last 150 days, it's on top of mind. And on the dark web, they're sure talking about how to exploit this. I heard Buffett the other day, and I think I heard this right because they got Geico talking about auto insurance. He says he's repricing now every six months. He wished he could reprice every month. I'm like, okay, that says the risk profile's changing. I heard the other day in the news that they had expected that the situation because of climate change with forest fires was going to be much greater 10 years down the road. Last year in California, it pulled forward that 10 years. So the risk profile's changing dramatically. How do you de-risk your business and your customers' businesses? Yeah, it's a great question. Insurance is a tricky product because you price it first and you learn how much it costs you a year later. And you use your experience in the past to forecast your experiences in the future. And then one thing we know about cyber with the rate in which technology changes is that that is never adequate. And what we found was that you could either try to reprice it every week and every month, which we obviously we do it for new accounts, but for existing policy holders, you went to a lot of effort to try and figure out what's the right price that represents the risk of a company. And then two months later, it's completely different. What do you do now? You definitely don't want to leave the company hanging without adequate coverage. And what we found was that if we step in and we help them fix the issues that they have, we can bring back the risks to its original levels. Some of the macro technology trends you mentioned, like AI, they represent a meaningful threat. We believe that we're going to see a significant uptick in social engineering and fraud. AI can impersonate a human in a way that is currently very crudely done by folks who are most of the times overseas, to try to impersonate American help desk providers and whatnot, not often very successfully. That's going to change and we will need to reassess, I think that the security of communication interfaces, whether email or in other ways, needs to improve dramatically. More accountability needs to be on the builders of the pipes. So if you provide an email solution, that solution needs to be a lot more robust. You can't just rely on a customer choosing to pay extra for security. Today, we're driving cars without seatbelts and we're telling people they can go and purchase a seatbelt for $25 a seat and most people don't. And I think that we probably need to bring that in-house. We might even need the government to apply a little bit of pressure here. How do people find you? How do you go to market? So we work with insurance brokers. Insurance brokers are the consultants that help companies understand what is the best solution out there and we partner with them to provide our products to customers. Once we bring them in as insurance customers, we then introduce our security team and we build a security relationship and we integrate our security products as well. And your security products, are they a combination of sort of organic products and sort of things that you OEM with some of the best of breed? Can you explain that? Yeah, so the most critical components in our offering, we build ourselves and then we partner with best of breed companies across all domains of security. So for example, this week we announced a partnership with Sentinel One on EDRs. We announced a partnership with MIMECAST on email security and it goes down the line with great companies across all important domains, identity access management and others. What are the most critical components that you want to have your own IP on? I think for us, the one area in security where we feel we are the most credible is in prioritizing which issue to go after first. It's because we are the ones who see at scale which issues get exploited by attackers. And so security industry has created frameworks with scoring and ways to try and quantify how critical is an issue. But they're all theoretical models. We use our own losses to score. You're real data. Actual data, and it's not just data, it's dollars that we spend. And we believe that the unit of measurement for risk is dollars and therefore everything we do, we measure in dollars. So that's the component that we want to bring in house and then the actual point solution that prevents or that blocks is probably where we would partner. You know the week leading up to RSA, you get inundated with reports as an analyst. And I was looking at one, I think it was Palo Alto Networks that showed a really interesting chart that 80% of the alerts come from 5% of the rules. Right, and so to your point about prioritization. You know, and this has been the case for years and years and years. It's always the same, the same, the same. You're saying you have IP because of your data and your information on actual loss that you can identify the ones that are most important. And I'll tell you, there's recommendation fatigue and security companies would only go to a certain extent to deliver a point where, because they still want to preserve the customer. Whereas we, when we feel we're going to lose a million dollars, we're going to be a little more intent in making sure that you understand what needs to be done and that you follow through. It's not always, I think it's, there needs to be a grown up here sometimes and the insurance company can play that role very effectively. People tend to also be more compliant when their insurance company calls. And I think that's an important job that needs to be done. So that brings me to my next question. There's certainly a narrative in the vendor community, the cybersecurity vendor community that we don't spend enough on security. And that the implication being if we spend more we'll be more secure. Should we? Is that true? I mean, because you're basically what you're saying is that you're more aligned with the customer because if you can eliminate the risk, the expected loss, you make more money. They spend less. So is spending more the answer? I think there are still meaningful gaps in security. Not all of them require spending more money. Some of them are better configuration. And using the tools you already have. A lot of people buy tools and then don't properly configure them and don't properly manage them. In some cases, there are definitely gaps that I would, as an example, anybody who's still using kind of endpoint protection and has not upgraded to EDRs, I would say absolutely upgrade to EDR. It's a meaningful de-risking. So spend there. Spend there. That's ROI. Absolutely. Other places just make use of MFA's and... It won't cost much. It won't cost much and make sure you secure your email environment. But I think that if we are successful in what we're doing we could potentially bring down the risk and with it the size of the category. But to me that wouldn't be a bad thing. So there's some $5 fixes that give you big ROI. The load denominator, high return. And then there are other areas where actually you get a faster ROI. It does make sense to spend. Yes. Rotem, great conversation. Thanks so much for coming on theCUBE. Thanks for having me. It's a pleasure. You're very welcome. All right, keep it right there. This is theCUBE's continuous coverage. Go to siliconangle.com. News is flooding the channel. We got all of our writers and journalists here. John Furrier, Dave Vellante. We'll be right back right after this short break from RSA 2023 from Moscone West.


In this lecture, we're going to summarise what we've learnt about communication signals and especially what we call the trade-offs between the different characteristics like the advantages and disadvantages. So a lot of it's going to be reviews, so I'm going to be flicking between some of the slides, the set of handouts that you've filled in, the signal equations and calculated some values and maybe a few new things. I'm going to try and summarise for signals, why do we care about bandwidth, what's the relationship with data rate, how do errors come into play and a few other concepts. The first thing I want to talk about is the relationship between bandwidth and data rate. What's the general rule or the trade-off? If we increase bandwidth, what happens to data rate? Up or down? Increase bandwidth, data rate goes up. That's our general rule that the more bandwidth we have, the more bits per second we can send. Given the other factors are the same, they do not change. So let's look at that with a simple example or an extension of the example we've looked at already. We've seen this one, I think if you go to this page, we've written a signal equation for this red signal, which has how many components, if you can remember? This one had two components, which means it was created from summing two sine waves together and they had particular frequencies, those two components and from that we could determine the bandwidth. So I'm going to use an equation for which produces a signal that looks like this one but I'm going to change the scale. This one was a scale under one second, I'm going to make a few changes but it's going to be a signal with two components. So this is the exact same shape but a different scale. Let's first write a general equation for this signal and note that, alright, so the signal S of t, two components, so we need two sine functions and remember the general equation for our sinusoid waves is 2 pi f t plus the phase. For simplicity the phase is going to be zero, it'll make our life easier, 2 pi f t, let's write it as 2 pi f t but there's a second component and the pattern that we used was that the second component would be one third the amplitude of the first and three times the frequency, 2 pi. If the frequency of the first component we denote as the variable f then the frequency of the second component we can write as 3f, just a general equation for this signal. We don't know f yet so f could be, take different values. I think in the example that we use we use f was 2 hertz, is that right? So you had something like sine 4 pi t, f was 2, so it becomes 4 pi t, one third sine 2 times pi times 3 times 2, f is 2, 12 pi t. But also we had an amplitude or a multiplier at the front of both of those signs of 4 over pi. That just changes the height, there's 4 over pi gave us a height of something like about 1.3. I'm going to leave that off just to save space because it could be any value, it could be 100 sine 2 pi f t plus 100 times a third sine 2 pi 3 f t, it would just change the scale on the vertical axis. But it's of not of interest in this example. So what we want to look at is the relationship between bandwidth and data rate. So let's try and given a particular bandwidth, see what data rate we can achieve. Let's say the bandwidth that we have BW is 2 kilohertz or 2,000 hertz. So our link or our transmission medium allows us to send only 2,000 hertz, a bandwidth of 2,000 hertz. We want to generate this signal. What frequency should we use? Such that the bandwidth is 2,000 hertz, again 1,000 hertz, why? The bandwidth is the difference between the maximum frequency component and the minimum. Here we only have 2, so it's the difference between the frequency of the 2 components. The first component is f, the second component is 3f. What's the difference? 2f. So in general, the bandwidth equals 2 times the frequency for this equation. We have a bandwidth of 2,000 hertz, so f should be set to 1,000 hertz. That's in fact the fundamental frequency of that signal. The signal shape repeats 1,000 times per second. What's the period of that signal? It repeats 1,000 times per second. How do you calculate the period? It's the inverse of the frequency, 1 divided by the frequency. So just 1 divided by 1,000, which is 1 millisecond on our plot. I will not draw it, but this point here would be 1 millisecond. It repeats every 1 millisecond, so the total duration of the plot will be 2 milliseconds. Now let's continue with our normal assumption that we've made in the past in that for half a period, when the signal is high most of the time, that represents a bit 1. And when the signal is low, it represents bit 0. So in this plot, there are in fact four bits transmitted, 1,0,1,0. What's the data rate? I'll just write it as dr for data rate. In one period, we transmit two bits in one period. So in this duration, there's a high bit 1 and a low bit 0. So two bits in that one period in this example. So two bits every 1 millisecond in one second, that means 2,000 bits, 2,000 bits per second. So just in this specific case, if we have a bandwidth of 2,000 hertz, we can achieve a data rate of 2,000 bits per second. Any questions yet? Just on this one. How did I know the one period transferred two bits? Good, that I defined that. I said that's what it is in this example. Because that would be defined by what we call the signal encoding technique. How do we map bits, 0s and 1s, to our or more generally data to our signal? Well, we need to define both at the transmitter and receive some scheme, some technique that says bit 1 is going to be represented by a high signal strength for half a period. Bit 0 is going to be represented by a low signal strength for half a period. But it could be different. We could have defined it as high then low represents bit 1, and although not on this plot, low then high represents bit 0. We could have defined it differently. But just in this example, high for half a period is one bit. We may come back to that and see the relationship of that technique shortly. Let's try the same shaped signal, but with a different bandwidth. Let's say double the bandwidth, 4,000 hertz. Same signal equation, what should the frequency be? It goes from F to 3F, a bandwidth of 2F. But we said the bandwidth will be 4,000. 4,000 equals 2F, F equals 2,000 hertz. So we'd achieve a frequency of 2,000 hertz. Period is 1 divided by the frequency, half a millisecond. And using the same signal encoding scheme, what's our data rate? In half a millisecond, we get two bits. So in one millisecond, we get four bits. So in 1,000 milliseconds or one second, we get 4,000 bits. What's the point here? Increasing the bandwidth increased our data rate. That's the point of this example. A couple of points to, so that's the key point from this example, but there's maybe some other things you notice. So yes, increasing bandwidth, if you went up to say 8,000 hertz, we can do it, 8,000 hertz bandwidth. That means the frequency must be what? 4,000 hertz, because it's 2F from 4,000 up to 12,000. Gives a bandwidth of 8,000. The period would be 1 quarter of a millisecond. And the data rate, 8,000 bits per second. Key point, increasing the bandwidth increases the data rate. Given other factors are the same, given we're using just two components, if we change the number of components, then the data rate may change in a different manner. But given everything else the same, higher bandwidth, higher data rate. Now, some things you may also notice. The data rate equals the bandwidth, apart from the units, 8,000, 8,000, 4,000, 4,000. Is that always true? No, that only happens because of our particular encoding scheme. I said one bit per half a period, or two bits per period. If we had a different scheme where it was one bit per period, instead of two bits per period, we'd get a different data rate. But the trend still applies. Increasing bandwidth increases data rate. What about increasing frequency? Turns out here also increasing frequency leads to an increased data rate. But we normally think of it from the bandwidth perspective. The bandwidth is what matters in practice. We usually need to select the bandwidth that we have available. We'd usually choose the frequency depending on the physical characteristics of where we want to transmit. If I want to transmit a signal that will go through walls, I would choose one frequency. If I want to transmit a signal that just maintained within a room or within a few centimeters, I may choose a different frequency. The bandwidth is usually chosen to minimize the range of frequencies we use to reduce the cost. So that's the thing that we care about. Increased bandwidth, increased data rate. That's our first trade-off. It's listed through some of the slides, but today we'll just, in one place, list all these trade-offs. So I'll write them down. You'll see this written down maybe in a couple of slides in the summary of the bandwidth and data rate section. And I'll say that's a good thing in that we normally would like to increase the data rate. We'd like to send as many bits as possible usually. So we think an advantage or a good thing about a communication system to get high data rate, use a higher bandwidth. Can everyone see the I there? Increase, move across a bit. Let's just list the trade-offs that we go through that we know already and a few new ones. What else have we seen in the past? If I go through to, if we go back to one of the previous examples on this handout, we can look quickly. We go up this one. Remember this one? For C and D, when we had this analog signal sending data, we had two different cases. The signal shape's about the same. The same signal element duration, 0.01 seconds. And we're just using, I think, the signal frequency is the same. If you look at the frequency of the sine wave, they're identical. What was the data rate for the first case? You've calculated it before. Remind us of the answer. So this is in the slides or the examples. What did you get? 100 bits per second, I think, we calculate the data rate in this case. We had a particular mapping that we defined. I think it was something like, for the signal element duration, if we transmit a wave that goes up first, that's a bit one, and down first is a bit zero. That was our signal encoding technique. And we got 100 bits per second. Then in example D, what data rate did we get? 200 bits per second. Because even though we have the same signal element duration, the same signal frequency, what we did differently is we said we have a different encoding technique. We said there are four different shapes. We had a phase of zero and a small amplitude, a phase of zero and a high amplitude. I think it was a phase of pi over two, such that it went down first and a high amplitude and a low amplitude and a phase of pi over two. We had four different signal elements to represent our data. And because we have four elements, in each element we can represent two bits at a time. So the result was in the signal element duration, compared to example C, we were sending two bits per signal element as opposed to one bit per signal element. We got a higher data rate, with all other factors being the same. How do we summarize that as a trade-off? The more signal elements to represent our data, the higher the data rate. In the first case, we had two different signal elements and we got 100 bits per second. In the second case, we had four different signal elements and we got 200 bits per second, all other factors being the same. If I wanted 300 bits per second, what would I do? Keeping all the other factors the same, how would I get 300 bits per second? How many signal elements would I use? How many different signal elements? Eight, eight signal elements with eight different values, we think we can represent a combination of three bits per each value, 000, 001, through to 111. There are eight combinations when we have three bits. So if we had eight different signal elements, we'd have three bit per signal element, therefore we'd get 300 bits per second, three bits per 0.01 seconds. More generally, we often refer to instead of the number of signal elements, we talk about levels of the signal. So in the first case, there are two levels because often we may show it as different magnitudes, but it doesn't have to be. But in general, we'd say this one, first case has two levels, two signal elements, the second one has four levels or four signal elements. And if we wanted 300 bits per second, we'd have eight levels or eight signal elements. Increasing the number of levels, keeping everything else the same, increases our data rate. Another key trade-off that we should be aware of. That is if we want a higher data rate, we can do two things. Increase the bandwidths and or increase the number of levels we use when we encode data to the signal. Let's keep going. Any questions on that one? Let's keep going and look at some other trade-offs that we've seen and some new ones. Click through. Remember we've gone through, we started with a single sine wave and then we had added two components together to get the red one. Then the signal three, we added a third component to get this green one and we kept going and we ended up with four components and then an example with 30 components and we got almost a square wave. Look at them, I can find them. Let's look at all four of those. Assuming all factors are the same, all we're doing here is increasing the number of components. Can anyone remember the spectrum of the red one? Two components, we had components at frequencies of two and six hertz. The component frequencies were two and six hertz and gave us a bandwidth of the difference between two and six, four hertz. So we've calculated that before. The green one, it was the first two components plus a third, two, six and 10, giving us a bandwidth of eight hertz. The fourth one, spectrum, we had two, six, 10 and 14 hertz giving us 12 hertz bandwidth and the bandwidth of the black one which had 30 components I calculated before. We will not do it. Anyone, did they calculate it? I think some people did. 116 or something, 116 hertz. You can check that, you can write down all 30 components and you see it goes from two up to 118 hertz. There were 30 components. So we're increasing the bandwidth here and we're using this scheme of, we're approximating ones and zeros as a high and low. Still the same scheme, one, zero, one, zero. They all represent the same sequence of four bits. So we can think each signal is approximating, setting a high signal for one and then low for zero. A square wave. Which of those four signals is the best approximation of a true square wave? The black one. This is closest visually to a true square wave. So we'd say it's the best approximation of what we really want, which was high, low, high, low. The red one is also high, low, high, low but it's not quite as accurate, we'd say. So a conclusion we make here is that increasing the number of components with all other factors being the same increases the bandwidth in fact. So increasing the bandwidth creates a signal which is more accurate in representing our data. The black one we'd say is more accurate than the red one in approximating the true square wave. Increasing bandwidth increases accuracy. Why do we care about accuracy? We know we care about data rate, how many bits per second, what's accuracy of relevance for? It's of relevance if things go wrong. If we have some noise, some impairments as well, the goal of the receiver is given the receive signal, map it back to the original data, the more accurate the signal, the less chance of making a mistake in mapping it back to the original data, the less chance of errors. If you have a less accurate signal like the red one, with some noise added into this, there's a more chance that the receiver will make a mistake and think for example, one level is the opposite and we'll get the wrong bits. So we say increasing the bandwidth increases the signal accuracy which reduces the errors. It decreases the chance of errors in that case. So that's why we care about accuracy, especially when we have impairments. So these are some things that we can do to improve our communications, to increase the data rate or decrease the errors. We've seen these trade-offs. Let's keep adding a few more. What's a bad thing about increasing the bandwidth? Cost, okay, increases the cost. What's a bad thing about increasing the number of levels? Going from two levels to four levels, we got a higher data rate. What's a disadvantage of using more levels? More complexity at the receiver, maybe it's harder to implement. That's true. What else? Because the receiver must interpret, both the transmitter and receiver must be encoded such that they will generate all of those levels. The more levels, the harder to implement. And the complexity means the algorithms to do it may take longer. So yes, correct. I'm not gonna write it down though. So he's correct that it may increase the complexity. But there's maybe a more significant thing when it comes to our data communications. I don't care too much about implementing it. You're all good programmers. You can implement things in an efficient manner. So let's ignore that for now. But something else. More levels decreases the accuracy. More importantly, increases the errors. Why? I don't think we have a good picture to illustrate. But with more levels, the receiver must correctly interpret what they receive to being one of those levels. This one we said we went from two levels to four levels. It doesn't show it very well. But the idea is that the more levels, when we add in some noise, some impairments, it means with more levels, there's less difference between each level. So with less difference between each level, there's less of a margin of error for us to make a mistake. Maybe we can try and draw that and to illustrate a very quick drawing. Let's say our levels are just in terms of magnitude. And let's consider a digital signal. Here's the first signal, two levels. Let's say this represents a one, zero, zero and one. So we see the mapping of high level to one, low level to zero, with a digital signal in this case. Let's use four levels. And let's first define the mapping. With four levels, we're gonna have something like very high, high or positive, low and very low. As opposed to our just in this case, high and low, or very high and very low. We would actually define the absolute magnitudes of those. Here we had high was one, low was zero. So we could have a different mapping here. Very high is one, one. High maybe one, zero. Low, zero, one and zero, zero. So now let's generate the same sequence of bits. We have one, zero. So we have a high signal. And then zero, one, which is a low signal. All right, so here's two examples of two levels versus four levels. And let's add some more data just to make it some more levels be in the example. The next two bits are one and one. And in our second scheme, that maps to very high. One, one. The first, the more levels, the higher the data rate. Within the same period of time, we can transmit more bits. We've already said that. More levels, higher data rate. The point we're trying to make is the more levels, the higher the chance of errors. Why? Because what the receiver has to distinguish in the second case is between the four different levels. So it receives a signal which is around here. Which level does it correspond to? Low or very low? There's only a small difference between the two when we have four different levels. So there's a more chance of making a mistake. Whereas with two levels, if it receives a signal which is around here, then it's highly likely that it's the low signal of zero. It's very unlikely to be a one. So when we take this same space and split it into more levels, there's a more chance that we'll make a mistake. More levels, higher data rate, but more levels increase the chance of errors. On average, we'd have more errors under the same conditions. We've got a few more to add, but let's return to the slides and talk about impairments. So the thing we finished on last lecture was transmission impairments. And we said there are different types of impairments, but two we're focusing on is attenuation and noise. And we'll go to the summary picture that captures both of them. Transmitter transmits a signal, the black one. As that signal propagates across some distance, it attenuates, it gets weaker. So the blue one is maybe it's the signal that's been attenuated. So it depends upon the distance by how much it attenuates, but it's going to be weaker, so a smaller amplitude. So if there was no noise, the receiver would receive the blue signal. But the other impairment that's significant is noise. Noise is all the other sources that the receiver receives in addition to the signal. So the receiver will receive the blue attenuated signal plus the red noise. And noise varies, there are different sources we mentioned. It's often seen as random variations because of the background noise, plus in some cases in this case I've drawn an impulse, maybe some short electrical disturbance leads to a peak. So there's some noise in the system. What the receiver gets is the summation of the noise and the attenuated signal, which is the purple one. And the receiver gets that received signal and maps it back to the data, assuming it was 1, 0, 1, 0 transmitted. The receiver measures the signal for each signal element duration. Measures here are high most of the time, must be a 1. Good. Measures here, and you have to zoom in to see, is it high or low? Well, for this part it's low, but for this part, because of that noise, it jumps to high. So it's possible that the receiver measures that and sees, well, the average value is high. It's a bit 1 I received. Then here it's high again, bit 1 received, then low, bit 0 received. 1, 1, 1, 0. Now there's a bit error. Transmitter was 1, 0, 1, 0. That noise may shift that second bit from a 0 to a 1, causing a bit error. So there's a problem of noise and attenuation. Of course, the more noise, the more chance of bit errors. If this noise is larger, it can flip the bits from low to high and vice versa. So there's a new trade-off. Increase noise, increase errors. That's a bad thing. So we'd like to have fewer errors. So that's a disadvantage, increasing noise. What else? What leads to more noise? Well, there are different sources of noise. There's noise, sort of background noise, or thermal noise. There's noise due to other transmitters. There's noise due to lightning strikes or other electrical disturbances or errors in the system. So they're different sources. Generally the background or the thermal noise, the larger the bandwidth we use, the more noise introduced. So this adds some more confusion between the trade-offs here. With a larger bandwidth, we usually get more noise. So see this. Increasing the bandwidth increases the noise, but we've just seen increasing the noise increases the errors, implies increasing the bandwidth increases the errors. But increasing the bandwidth decreases the errors. That's confusing. We haven't said by how much. So we haven't said increases the errors by 10% or doubles. In fact, to compare all of these trade-offs, we should really look at by how much does it increase the errors to be able to see whether, yes, increasing the bandwidth from the signal perspective decreases the errors, but increasing the bandwidth allows for more noise, which can increase errors. To know whether we get a total increase or a total decrease of errors, we need to know how much they change them. But we're not going to look at that in this topic. But as people who design and select communication systems would need to analyse that in depth and see, okay, we want high bandwidth for fewer errors because of the signal. We can have more components in the signal. But the more bandwidth we add, the more chance or the more noise comes in. So we need to make sure that we don't allow too much noise in to increase the errors to overcome the game we get from the better signal. This decrease of errors was due to the more components in the signal, the higher signal accuracy. This increase in errors is due to noise, but two different factors. So there's a trade-off there. How do we overcome noise? Let's say it's very quiet, there's not so many students here, but this morning in the lecture, many students, many students talking, how do I overcome noise? What do you think I can do? Assuming I can't control the students from talking, they don't listen to me. Not change my frequency, change sport. Talk louder. I could change my volume or my signal strength. I could talk louder or turn up the amplifier to overcome that noise. So that's another factor that is if we transmit with a higher signal strength with respect to the noise, we can increase the amount of data we receive or decrease the amount of errors that occur due to noise. So that's a good thing or a way that we can improve performance. I say increase the signal that the receiver receives, the strength I mean, the signal strength or power. We will see an equation shortly that it can increase data rate. Will I fit it in? You will see. Increasing the signal strength can effectively increase the data rate. Note that errors and data rate are related. If I have a data rate of 1,000 bits per second and an error rate of 10%, I transmit 1,000 bits per second, but 10% of those bits received are in error. 100 bits are received in error. Effectively, I've only really transmitted 900 bits. So given a particular data rate, say 1,000 bits per second, if of those 1,000 bits received 100 or wrong, means 900 are correct. So really my data rate is 900 bits per second, my effective data rate. So in fact, when we decrease the errors, we're really increasing the data rate as well. We transmit with a higher signal strength to overcome the effects of noise. What's the problem with increasing my signal strength? I turn up my microphone. What happens? Well, different things may happen. There may be some distortion if I turn it up too high, but we haven't talked about distortion. There's a class next door. If I turn up my microphone, then they start to hear my signal and I create noise on them. So I'm interfering. We say this is interference on some other entities communicating. Cross talk or interference is what it's called. So increasing your signal strength can also increase noise. Usually noise on others, which increases errors. More noise, more errors. Increase the signal, less errors. So we need to be able to measure those values and how much to determine under what cases should we have a high signal and what cases should we have a high bandwidth. Right. So increasing the signal helps us but impacts upon someone else. Now, if we consider the entire communication system, that may have a negative impact in total. That was shown on this slide. This co-channel interference or interference in general, or cross talk. Two transmitters wanting to send to two separate receivers TX1 to RX1, TX2 sending the green signal to RX2 but they interfere with each other. So RX1 receives the blue signal from TX1 but it also receives interference from TX2 which is in fact the green signal. And they add together and given attenuation this is what RX1 receives and you can see it's not a good representation of what it was TX1 intended it to receive. The interference will result in errors at the receiver. It would not know what bits were transmitted. And similar for RX2. So this is what we sometimes call in wireless systems interference and in wired systems it's usually referred to as cross talk. It can happen with two different wires that they can also interfere with each other. The energy dissipates out of the wire and onto others. I think we've got most of the trade-offs there. But you can see that they are conflicting in some cases. It's not simple as let's just increase the bandwidth. We must consider several factors. It's complex. Any questions on those trade-offs before we move on to the last part of this data transmission topic? You may have a look at this example. We will not go through it now. It's just an example if we transmit some data or a particular signal and then we add in noise. This is what we receive. So we receive this signal and what the receiver does is then maps that by sampling is the signal low if so and be careful. In this case a low signal represents a bit one the opposite of what we've used. High signal bit zero. And what the receiver does it samples. Okay, the signal here is low then for I've received a bit one. That's correct because bit one was sent and it keeps going. At this point it samples and it measures the signal strength to be positive. High. High means bit zero received. That's a bit error because in fact bit one was transmitted. So this is just showing the impact of noise. It leads to bit errors. These two slides we're going to skip over. We may return to them in the next topic on transmission media. They just introduced some notation about transmit power and a few other factors but we'll introduce them when necessary. They're not necessary at the moment. To finish this topic of our trade-offs that we've listed we said they don't indicate by how much we increase the data rate. By how much do we increase or decrease the number of errors. We would like some equations that tell us by how much. Well it turns out that people have developed some equations and two famous and rather simple equations to tell us a relationship between data rate, bandwidth and some other factors. And that's what we talked about as channel capacity. What do we mean by channel capacity? Capacity we mean the maximum data rate we can achieve. In the same way that the capacity of this lecture room is 60 students. The current number of students is 12. So with both cases counting number of students capacity is the maximum we can fit in. In a data communications data rate measures bits per second the capacity is the maximum number of bits per second we can send in some communication system. And the channel is the thing that is characterised by a particular bandwidth a particular frequency usually. So a link is a simpler way to think of a communication channel. We've seen the trade-offs, they're complex. Let's look at two equations that combine some of them together. They're called the Nyquist capacity equation and the Shannon capacity equation. We'll go through each of them with some examples. Mr Nyquist did analysis of communication systems and come up with this equation in the centre of the slide. C equals 2B log base 2 of M. His analysis assumes that there is no noise. Let's assume that the noise is so low so insignificant that we can say it's zero. Now there is never no noise. There's always some noise. But to make the analysis simple he assumes there's no noise. In such a case he determined that the data rate or capacity C for capacity measured in bits per second is equal to 2 times the bandwidth measured in hertz times log base 2 of the number of levels M. M is the number of levels in our signal that we use. Remember the equation and know how to use it and we'll see how to use it with a simple example. Everyone remember dial-up modems? No? Can anyone remember dial-up modems as the one that made the strange sound when you connected? Anyone seen it in a movie or something? A dial-up modem? No? Everyone's getting a little bit too young. So before ADSL modems we had dial-up modems that basically similar to an ADSL modem you connect your telephone line into it from the wall the telephone line comes in and connect your computer to the modem. Sometimes the modem was built into the computer. The point is that the modem takes you the data from your computer and sends it as an analog signal across the telephone system, across the telephone line and it sends it to your ISP, your internet service provider. And the telephone system was designed to support a bandwidth of 3,100 hertz. So the signal transmitted across the telephone line had a bandwidth of 3,100 hertz. Why? Why would a telephone line support a bandwidth of 3,100 hertz? Anyone want to guess? Telephones have been around for 100 years or so. What have they used for mainly? What data is communicated with telephones? Voice. The typical bandwidth of a human voice is about 3,000 hertz. When we speak it ranges from hundreds of hertz up to about 3 or 4 kilohertz. So the telephone system was designed only to carry that range of frequencies. But now we want to connect our computer and send bits, not just voice. So we have a bandwidth of 3,100 hertz. What's the maximum data rate we can achieve with our dial-up modem? Well, let's start. Let's assume our basic signal scheme of high for bit one, low for bit zero. Find the data rate. And the hint, use the Nyquist capacity equation. I shouldn't have labelled them A and B. A is your modem. B in this picture is your, say, the modem of the ISP, your internet service provider. B, sorry, here is bandwidth in this Nyquist equation. It's not location B. We have a link between the modem and the internet service provider. That link allows us to send signals with a bandwidth of 3,100 hertz. Let's assume that we use a signalling technique that gives us just two levels. High for bit one, low for bit zero, for example, or the opposite. What's the maximum data rate we can achieve using this modem? Well, the Nyquist capacity equation. Just plug in the values. The capacity, the maximum data rate, is two times the bandwidth times log base two of the number of levels in our signalling coding technique. Two times 3,100, 6,200. Log base two of two is, if I remember your logarithms, two to the power of something equals two, one. So it's just become 6,200 bits per second. Bandwidth is measured in cycles per second or hertz. Here we get bits per second. Capacity or data rate. So that's just an application of the Nyquist capacity equation. It says, if we have a channel with a bandwidth of 3,100 hertz, which is your typical telephone system, you can't send more than 6.2 kilobits per second if you use this signalling coding technique. You can't go higher. There's no way under these conditions. And this assumes there's no noise. If there was noise, you wouldn't even get this level. It'd be less. No one remembers the dial-up modems, so no one's going to remember what was the higher speed that they got. If you go back in history and find one of the most recent dial-up modems, they got to a speeds of about 56 kilobits per second. When you bought one, 56 kilobits per second using a telephone line. But we just said that our capacity is 6.2 kilobits per second. How did we, those modems, get a speed of 56 kilobits per second? What did they do? We said that we got a... The maximum is 6,200 bits per second, but I'm telling you, the real modems, they could get up to about 66 kilobits per second. So, not frequency, look at the Nyquist equation. Use higher or lower, what? bandwidth we can't change. Bandwidth is a characteristic of that telephone line. If we change... and use optical fiber, maybe we can change the bandwidth. But if we want to use our telephone network with the old modems, we're stuck with 3,100 hertz. So we change what? M, the number of levels. Find the number of levels necessary to get 56 kilobits per second. So if C is 56 kilobits per second, find M. How many levels did that modem use? Assuming no noise, how many levels would be needed? Well, we know C, we know the bandwidth, we don't know M. And you need your calculator there. To find M, let's find at least log base 2 of M. So we've got 56,000 equals 2 times 3,100 times log base 2 of M. Let's rearrange. So 56,000 divided by 2 divided by 3,100 gives us about 9. Let's approximate to 9. That's a nice number here, very close to 9. I think it wasn't exactly 56 kilobits per second, it was maybe 55 points, something, something. So let's say that gives us 9. Rearranging, log base 2 of M is 9, therefore M is maybe logarithms and exponentials. Log base 2 of M is 9, therefore M equals 2 to the power of 9. 512. So those dial-up modems that supported about 56 kilobits per second, what would they do is they would transmit a signal of a level of out of 512 possible levels. When they transmit a signal, that signal element represents 9 bits at a time. And with the same bandwidth, we get a speed up to our 56 kilobits per second. How can we increase further? Okay, so what happened is that with the dial-up modems we're getting 56 kilobits per second. It turns out to increase that using the same bandwidth is very hard because let's move up. Here we have 9 bits per level, or 512 levels. So the next one up would be 10 bits per level. How many levels? If we try to increase the capacity, if we went up to M equal to 1024 to get 10 bits per level, then it would become which is 10, which gives us what, 62 kilobits per second. So increasing the capabilities of our modem, getting a new modem which handles double the number of levels, so it's complex, more chance of errors gives us an increase from 56K up to 62K. And at that point in time another 6 kilobits per second was insignificant. To get that extra 6 kilobits per second you have to go to a lot of effort. And it turned out that people come up with a new technology which ADSL is one of the variants that we use. ADSL doesn't necessarily increase the levels. ADSL transmits a signal which uses not just the voice frequency of the telephone system, it uses a range of other frequencies that can also be sent across the copper wires. So yes, the telephone system was designed to support carrying voice about 3 kilohertz, but the copper cabling inside your telephone network can carry a much wider range of frequencies than one or two megahertz. So that's what ADSL does. It transmits a signal up to about one megahertz. Increasing B to one megahertz you can see you can get a jump in the data rate. So the new technology allowed different types of signals utilised a higher bandwidth. So Nyquist Equation relates data rate to the bandwidth and the number of levels in the signal scheme we use. It assumes there's no noise. In reality there is some noise and that's effectively going to decrease the data rate below the capacity we calculate. We said it's 56 kilobits per second but with noise it's going to be less in practice. But maybe only slightly less. So to take into account noise Claude Shannon did analysis and come up with another relationship that is maximum data rate C, bandwidth B but instead of looking at the number of signal levels focusing on the signal and the noise power the amount of noise especially and denote it as SNR which is signal to noise ratio and the equation is above that. Signal to noise ratio like the name suggests is the ratio between the signal received the strength of the signal received and the strength of the noise received. We said increasing the signal can increase the data rate. That was one of the trade-offs we noted we tried to explain that that is the stronger the signal you receive relative to the noise you receive when the signal power received goes up because for example I turn up the volume then the signal to noise ratio goes up. If the noise is the same but the signal goes up the ratio goes up and as the signal to noise ratio goes up the capacity goes up. Higher signal power with everything else the same higher capacity. And the other trade-off we saw we said increasing noise increases errors and another thing of increasing errors is decreases data rate. More people start talking in the background more noise if the noise goes up that you hear this ratio goes down if the denominator goes up then the ratio goes down and if the ratio goes down the capacity goes down. Higher signal higher capacity more noise lower capacity. That's what it shows there. So let's see it in our last example see it being used this equation and we'll modify this one a little bit. We have a channel that uses a spectrum of between 3 MHz and 4 MHz. What does that tell you? The first phrase bandwidth is 1 MHz. The spectrum from 3 up until 4 bandwidth is the difference. The bandwidth is 1 MHz. With a signal to noise ratio and here's where we'll change it in this question I used decibels dB but we haven't talked about them so we'll change it with a signal to noise ratio delete the dBs for now and set the value to be 251 in a later topic we'll explain how to convert from an absolute value to a decibel value but if you convert to 24 dB it's equivalent to a ratio of 251 we'll see that later 251 so change that and now the question is how many signal levels are required to achieve the Shannon capacity there are two steps how many signal levels well that hints we need to use Nyquist capacity somewhere because Nyquist includes M in the equation but to achieve Shannon capacity we must also first use the Shannon capacity equation so let's first find the Shannon capacity in such a channel bandwidth 1 MHz SNR 251 plug it into the equation so x sending to y in this case we have a link or a communication channel we have a bandwidth of 1 MHz and a signal to noise ratio of 251 we'll plug it into the equation in a moment but let's first explain what does this SNR of 251 mean well quite simply it means that the signal received if we measure the strength it's 251s times greater than the noise received so x transmits a signal y receives that signal let's say we measured the power levels and the received signal with another s just as an example let's say it's received at a strength and I measure it 502 milliwatts so y the computer y receives the signal and it's got some measurements of the signal strength signal strength can be measured in volts or watts you know watts in milliwatts and y measures the received signal to be 502 milliwatts and it also measures the received noise so at a different time it's measured how much noise it receives how much noise what's the value of noise I received the actual signal which is the data that x send has a strength of 502 milliwatts but I also receive other signals which is the noise what's the strength of the noise 2 2 milliwatts given the signal to noise ratio is 251 it means the signal must be 251 times larger than the noise so the noise must be 2 milliwatts in this case note that the signal to noise ratio is a ratio it's dimensionless there's no units here it's simply 251 so that's just an example of what the SNR means if the signal received 251 microwatts then the noise would be 1 microwatts and we'd have the same SNR signal to noise ratio the capacity equation from Shannon only cares about the ratio between those values not the absolute value now let's use the equation what we call the Shannon capacity will be we know is 1 megahertz 1 million 1 by 10 to the power of 6 log base 2 1 plus 251 approximately so all I did was replace B with 1 million and SNR with 251 log base 2 of 252 is about about remember your powers of 2 2 to the power of 8 is 256 256 and 252 very similar so log base 2 of 252 is about 8 slightly less so we get 8 times 1 million 8 megabits per second approximately approximately 8 megabits per second note that the bandwidth is in hertz or megahertz in this case the capacity or data rate is in bits per second megabits per second the question was how many levels do we need to achieve the Shannon capacity what is the Shannon capacity 8 megabits per second how many levels do we need to achieve that use Nyquist capacity we want to know M we already know the bandwidth the channel is still 1 megahertz and we also know the capacity it's 8 megabits per second 8 megabits, 8 million equals 2 times the bandwidth which is 1 million, 2 million so log base 2 of M equals 8 divided by 2 equals 4 M equals 16 2 to the power of 4 is 16 so this is just saying that given that particular channel where we knew the signal to noise ratio we knew we could achieve up to 8 megabits per second to do that we must use a signal that encodes with at least 16 levels if we use less let's say 8 levels there's no way that we can get 8 megabits per second even with no noise so it just combines the two in an example and that's a good place to finish we've covered the trade-offs amongst the different characteristics of signals and we've finished with two specific cases of those trade-offs relating data rate and other characteristics using Shannon and Nyquist capacity equations