A Survey on Space-Time Turbo Codes
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paper_title: Turbo Trellis Coded Modulation with Iterative Decoding for Mobile Satellite Communications

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Ab.wrmvIn this paper, analytical bounds on the performance of parallel concatenation of two codes, known as turbo codes, and serial concatenation of two codes over fading channels are obtained. Based on this analysis, design criteria for the selection of component trellis codes for MPSK modulation, and a suitable bit-by-bit iterative decoding structure are proposed. Examples are given for throughput of 2 bitdsedftz with 8PSK modulation. The parallel concatenation exam. ple uses two rate 4/5 8-state convolutional codes with two interleaves. The convolutional codes outputs are then mapped to two 8PSK mod. ulations. The serial concatenated code example uses an 8-state outer code with rate 4/5 and a 4-state inner trellis code with 5 inputs and 2x8PSK outputs per trellis branch. Based on the above mentioned design criteria for fading channels, a method to obtain the structure of the trellis code with maximum diversity is proposed. Simulation results are given for AWGN, and independent Rayleigh fading channel with perfect Channel State Information (CSI).
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paper_title: A space-time coding modem for high-data-rate wireless communications

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This paper presents the theory and practice of a new advanced modem technology suitable for high-data-rate wireless communications and presents its performance over a frequency-flat Rayleigh fading channel. The new technology is based on space-time coded modulation (STCM) with multiple transmit and/or multiple receive antennas and orthogonal pilot sequence insertion (O-PSI). In this approach, data is encoded by a space-time (ST) channel encoder and the output of the encoder is split into N streams to be simultaneously transmitted using N transmit antennas. The transmitter inserts periodic orthogonal pilot sequences in each of the simultaneously transmitted bursts. The receiver uses those pilot sequences to estimate the fading channel. When combined with an appropriately designed interpolation filter, accurate channel state information (CSI) can be estimated for the decoding process. Simulation results of the proposed modem, as applied to the IS-136 cellular standard, are presented. We present the frame error rate (FER) performance results as a function of the signal-to-noise ratio (SNR) and the maximum Doppler frequency, in the presence of timing and frequency offset errors. Simulation results show that for a 10% FER, a 32-state eight-phase-shift keyed (8-PSK) ST code with two transmit and two receive antennas can support data rates up to 55.8 kb/s on a 30-kHz channel, at an SNR of 11.7 dB and a maximum Doppler frequency of 180 Hz. Simulation results for other codes and other channel conditions are also provided. We also compare the performance of the proposed STCM scheme with delay diversity schemes and conclude that STCM can provide significant SNR improvement over simple delay diversity.
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paper_title: Signal design for transmitter diversity wireless communication systems over Rayleigh fading channels

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Transmitter diversity wireless communication systems over Rayleigh fading channels using pilot symbol assisted modulation (PSAM) are studied. Unlike conventional transmitter diversity systems with PSAM that estimate the superimposed fading process, we are able to estimate each individual fading process corresponding to the multiple transmitters by using appropriately designed pilot symbol sequences. With such sequences, special coded modulation schemes can then be designed to access the diversity provided by the multiple transmitters without having to use an interleaver or expand the signal bandwidth. The code matrix notion is introduced for the coded modulation scheme, and its design criteria are also established. In addition to the reduction in receiver complexity, simulation results are compared to, and shown to be superior to, that of an intentional frequency offset system over a wide range of system parameters.
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paper_title: A new view of performance analysis techniques in correlated Rayleigh fading

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This paper provides a new formulation for the pair-wise error probability for any coherently demodulated system in flat Rayleigh fading. The novelty of the result is that the resulting error rate expression is a polynomial function of the eigenvalues of a 'signal' matrix. This view also enables a simple new asymptotically tight bound on the pair-wise error probability. Examples of single and multiple transmit antenna systems are considered.
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paper_title: Space-time codes for high data rate wireless communication: Performance criterion and code construction

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We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. We derive performance criteria for designing such codes under the assumption that the fading is slow and frequency nonselective. Performance is shown to be determined by matrices constructed from pairs of distinct code sequences. The minimum rank among these matrices quantifies the diversity gain, while the minimum determinant of these matrices quantifies the coding gain. The results are then extended to fast fading channels. The design criteria are used to design trellis codes for high data rate wireless communication. The encoding/decoding complexity of these codes is comparable to trellis codes employed in practice over Gaussian channels. The codes constructed here provide the best tradeoff between data rate, diversity advantage, and trellis complexity. Simulation results are provided for 4 and 8 PSK signal sets with data rates of 2 and 3 bits/symbol, demonstrating excellent performance that is within 2-3 dB of the outage capacity for these channels using only 64 state encoders.
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paper_title: A Simple Transmit Diversity Technique for Wireless Communications

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This paper presents a simple two-branch transmit diversity scheme. Using two transmit antennas and one receive antenna the scheme provides the same diversity order as maximal-ratio receiver combining (MRRC) with one transmit antenna, and two receive antennas. It is also shown that the scheme may easily be generalized to two transmit antennas and receive antennas to provide a diversity order of 2. The new scheme does not require any bandwidth expansion any feedback from the receiver to the transmitter and its computation complexity is similar to MRRC.
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paper_title: Space-time block coding for wireless communications: performance results

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We document the performance of space-time block codes, which provide a new paradigm for transmission over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a space-time block code, and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. Maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection. This uses the orthogonal structure of the space-time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver. We review the encoding and decoding algorithms for various codes and provide simulation results demonstrating their performance. It is shown that using multiple transmit antennas and space-time block coding provides remarkable performance at the expense of almost no extra processing.
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paper_title: Combined array processing and space-time coding

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The information capacity of wireless communication systems may be increased dramatically by employing multiple transmit and receive antennas. The goal of system design is to exploit this capacity in a practical way. An effective approach to increasing data rate over wireless channels is to employ space-time coding techniques appropriate to multiple transmit antennas. These space-time codes introduce temporal and spatial correlation into signals transmitted from different antennas, so as to provide diversity at the receiver, and coding gain over an uncoded system. For large number of transmit antennas and at high bandwidth efficiencies, the receiver may become too complex whenever correlation across transmit antennas is introduced. This paper dramatically reduces encoding and decoding complexity by partitioning antennas at the transmitter into small groups, and using individual space-time codes, called the component codes, to transmit information from each group of antennas. At the receiver, an individual space-time code is decoded by a novel linear processing technique that suppresses signals transmitted by other groups of antennas by treating them as interference. A simple receiver structure is derived that provides diversity and coding gain over uncoded systems. This combination of array processing at the receiver and coding techniques for multiple transmit antennas can provide reliable and very high data rate communication over narrowband wireless channels. A refinement of this basic structure gives rise to a multilayered space-time architecture that both generalizes and improves upon the layered space-time architecture proposed by Foschini (see Bell Labs Tech. J., vol.1, no.2, 1996).
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paper_title: Detection algorithm and initial laboratory results using V-BLAST space-time communication architecture

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The signal detection algorithm of the vertical BLAST (Bell Laboratories Layered Space-Time) wireless communications architecture is briefly described. Using this joint space-time approach, spectral efficiencies ranging from 20-40 bit/s/Hz have been demonstrated in the laboratory under flat fading conditions at indoor fading rates. Early results are presented.
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paper_title: On limits of wireless communications in a fading environment when using multiple antennas

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This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bit-rates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multi-element array (MEA) technology, that is processing the spatial dimension (not just the time dimension) to improve wireless capacities in certain applications. Specifically, we present some basic information theory results that promise great advantages of using MEAs in wireless LANs and building to building wireless communication links. We explore the important case when the channel characteristic is not available at the transmitter but the receiver knows (tracks) the characteristic which is subject to Rayleigh fading. Fixing the overall transmitted power, we express the capacity offered by MEA technology and we see how the capacity scales with increasing SNR for a large but practical number, n, of antenna elements at both transmitter and receiver. ::: ::: We investigate the case of independent Rayleigh faded paths between antenna elements and find that with high probability extraordinary capacity is available. Compared to the baseline n = 1 case, which by Shannon‘s classical formula scales as one more bit/cycle for every 3 dB of signal-to-noise ratio (SNR) increase, remarkably with MEAs, the scaling is almost like n more bits/cycle for each 3 dB increase in SNR. To illustrate how great this capacity is, even for small n, take the cases n = 2, 4 and 16 at an average received SNR of 21 dB. For over 99% of the channels the capacity is about 7, 19 and 88 bits/cycle respectively, while if n = 1 there is only about 1.2 bit/cycle at the 99% level. For say a symbol rate equal to the channel bandwith, since it is the bits/symbol/dimension that is relevant for signal constellations, these higher capacities are not unreasonable. The 19 bits/cycle for n = 4 amounts to 4.75 bits/symbol/dimension while 88 bits/cycle for n = 16 amounts to 5.5 bits/symbol/dimension. Standard approaches such as selection and optimum combining are seen to be deficient when compared to what will ultimately be possible. New codecs need to be invented to realize a hefty portion of the great capacity promised.
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paper_title: Space-time block codes: a capacity perspective

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Space-time block codes are a remarkable modulation scheme discovered recently for the multiple antenna wireless channel. They have an elegant mathematical solution for providing full diversity over the coherent, flat-fading channel. In addition, they require extremely simple encoding and decoding. Although these codes provide full diversity at low computational costs, we show that they incur a loss in capacity because they convert the matrix channel into a scalar AWGN channel whose capacity is smaller than the true channel capacity. In this letter the loss in capacity is quantified as a function of channel rank, code rate, and number of receive antennas.
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paper_title: Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas

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This paper addresses digital communication in a Rayleigh fading environment when the channel characteristic is unknown at the transmitter but is known (tracked) at the receiver. Inventing a codec architecture that can realize a significant portion of the great capacity promised by information theory is essential to a standout long-term position in highly competitive arenas like fixed and indoor wireless. Use (n T , n R ) to express the number of antenna elements at the transmitter and receiver. An (n, n) analysis shows that despite the n received waves interfering randomly, capacity grows linearly with n and is enormous. With n = 8 at 1% outage and 21-dB average SNR at each receiving element, 42 b/s/Hz is achieved. The capacity is more than 40 times that of a (1, 1) system at the same total radiated transmitter power and bandwidth. Moreover, in some applications, n could be much larger than 8. In striving for significant fractions of such huge capacities, the question arises: Can one construct an (n, n) system whose capacity scales linearly with n, using as building blocks n separately coded one-dimensional (1-D) subsystems of equal capacity? With the aim of leveraging the already highly developed 1-D codec technology, this paper reports just such an invention. In this new architecture, signals are layered in space and time as suggested by a tight capacity bound.
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paper_title: V-BLAST: an architecture for realizing very high data rates over the rich-scattering wireless channel

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Information theory research has shown that the rich-scattering wireless channel is capable of enormous theoretical capacities if the multipath is properly exploited. In this paper, we describe a wireless communication architecture known as vertical BLAST (Bell Laboratories Layered Space-Time) or V-BLAST, which has been implemented in real-time in the laboratory. Using our laboratory prototype, we have demonstrated spectral efficiencies of 20-40 bps/Hz in an indoor propagation environment at realistic SNRs and error rates. To the best of our knowledge, wireless spectral efficiencies of this magnitude are unprecedented and are furthermore unattainable using traditional techniques.
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paper_title: Trellis-coded modulation and transmit diversity: design criteria and performance evaluation

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This paper presents the selection criteria for trellis codes used with the simple transmit diversity scheme proposed in Alamouti (1998) and reviewed in this paper. The optimum metrics for soft decision Viterbi decoding are derived and the asymptotic coding gains are calculated. The design method achieves both coding gain and a diversity order of 2 using 2 transmit antennas and 1 receive antenna. It is also demonstrated that trellis codes optimized for AWGN are also optimal for use in conjunction with the transmit diversity scheme in Rayleigh fading.
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paper_title: Frequency-Domain Receivers for Rate-1 Space-Time Block Codes

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This paper considers iterative frequency-domain receivers for block transmission techniques with rate-1 Space Time Block Coding (STBC) for two and four transmit antennas using both Orthogonal Frequency Division Multiplexing (OFDM) and Single-Carrier (SC) schemes. The proposed receiver includes an interference canceller which enhances the performance of the non-orthogonal STBC scheme with 4 transmit antennas, allowing performances close to those of orthogonal codes. Our performance results show that combining STBC with block transmission techniques allows excellent performances.
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paper_title: Unitary space-time modulation for multiple-antenna communications in Rayleigh flat fading

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Motivated by information-theoretic considerations, we propose a signaling scheme, unitary space-time modulation, for multiple-antenna communication links. This modulation is ideally suited for Rayleigh fast-fading environments, since it does not require the receiver to know or learn the propagation coefficients. Unitary space-time modulation uses constellations of T/spl times/M space-time signals (/spl Phi//sub i/, l=1, ..., L), where T represents the coherence interval during which the fading is approximately constant, and M<T is the number of transmitter antennas. The columns of each /spl Phi//sub i/ are orthonormal. When the receiver does not know the propagation coefficients, which between pairs of transmitter and receiver antennas are modeled as statistically independent, this modulation performs very well either when the signal-to-noise ratio (SNR) is high or when T/spl Gt/M. We design some multiple-antenna signal constellations and simulate their effectiveness as measured by bit-error probability with maximum-likelihood decoding. We demonstrate that two antennas have a 6-dB diversity gain over one antenna at 15-dB SNR.
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paper_title: Space-time processing for broadband wireless access

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We present an overview of research activities on space-time coding for broadband wireless transmission performed at AT&T Shannon Laboratory over the past two years. The emphasis is on physical layer modem algorithms such as channel estimation, equalization, and interference cancellation. However, we also discuss the impact of space-time coding gains at the physical layer on throughput at or above the networking layer. Furthermore, we describe a flexible graphical user interface attached to our physical layer simulation engine in order to explore the performance of space-time codes under a variety of practical transmission scenarios. Simulation results for the EDGE cellular system and the 802.11 wireless LAN environment are presented.
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paper_title: Design and Standardization of Low-Density Parity-Check Codes for Space Applications

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In the last decade, a family of 16 low-rate turbo codes were designed and standardized, and decoders were built for each of the three ground complexes of the Deep Space Network (DSN). These codes are now flying on several missions, including MRO, MESSENGER, and STEREO. A brief summary of the turbo code family is presented, along with a performance and complexity comparison to NASA’s legacy codes. In the last few years, exciting research developments have produced ten higher rate low-density parity-check (LDPC) codes for the high-data-rate missions anticipated in the coming decades. Originally invented by R. Gallager in his PhD thesis in 1960, this coding technique was largely forgotten for more than 30 years. The primary advance in LDPC codes is the discovery of an iterative decoding algorithm, now called Belief Propagation (BP) decoding, which offers near-optimum performance for large linear LDPC codes at a manageable complexity. The performance gains of LDPC codes were difficult to realize technologically in the early 1960s. Several decades of VLSI development have finally made the implementation of these codes practical. The renaissance of LDPC codes did not mark the end of turbo codes, however. LDPC codes have performance and complexity advantages over turbo codes at high code rates, but turbo codes are currently still the best solution for the lower code rates. This natural partition means that the standard family of turbo codes at rates 1/6, 1/4, 1/3, and 1/2 can live in harmony with a proposed standard of LDPC codes at rates 1/2, 2/3, 4/5, and 7/8. LDPC codes hold the promise of significantly lower decoding complexity and error-floors than turbo codes, while still achieving near-capacity performance. A summary is presented of the performance and complexity of the LDPC code family and related codes developed by NASA, along with a description of recent FPGA implementations at speeds in excess of 100 Msps. Synchronization aspects at low SNR are also discussed, and the status of infusion of this new technology in NASA missions is addressed. Standardization of LDPC codes by the CCSDS has proven challenging. In part, this is because the class of LDPC codes is very large, and their differences can be small. There is also a long list of desirable attributes, and no code is superior in all categories. The status of the standardization process is described, including a discussion of the advantages and disadvantages of the proposed candidates.
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paper_title: Application of space-time coding techniques in third generation systems

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We consider the application of space-time processing techniques using multiple antennas to third generation mobile communication systems, which have been shown to enable substantial capacity improvements. We describe a technique for the evaluation of such schemes and apply it to some potential applications of the technique within the current third generation standards. We describe a simple technique which can provide a 16/sup th/ order diversity improvement, resulting in a 10 dB performance improvement.
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paper_title: Improving BLAST performance using space-time block codes and turbo decoding

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An architecture that theoretically achieves channel capacity on multi-input multi-output channels was proposed by Foschini (1996) as BLAST. We show that in practical systems BLAST performance is limited by error propagation. The theoretically possible increase in diversity level during successive detection steps cannot be achieved. We evaluate the possibilities to improve BLAST performance. We first analyze an MMSE solution compared to zero forcing. Furthermore, we show the benefits of soft over hard interference cancellation and propose an iterative turbo detection algorithm. Finally, we apply transmit diversity with space-time block codes to BLAST. This improves the overall diversity level and reduces the number of required receive antennas.
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paper_title: Recursive space-time trellis codes using differential encoding

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Differential space-time modulation (DSTM) has been recently proposed by Hughes, and Hochwald and Sweldens when the channel information is not known at the receiver. On the other hand, the DSTM also needs a recursive memory of a matrix block at the encoder and therefore provides a trellis structure when the channel information is known at the receiver, which is the interest of this paper. This recursive structure of the DSTM has been adopted lately by Schlegel and Grant as an inner trellis code concatenated with an outer binary code to achieve turbo gain. The number of states of the trellis from the recursive structure depends on both the memory size, which is fixed in this case, and the unitary space-time code (USTC). In this paper, we propose a new USTC design criterion to ensure that the trellis structure improves the diversity product over the USTC as a block code. Based on the new criterion, we propose a new class of USTC design for an arbitrary number of transmit antennas that has an analytical diversity product formula for two transmit antennas. We then follow Schlegel and Grant's approach for joint encoding and iterative decoding of a binary coded DSTM (turbo space-time coding) and numerically show that our new USTC designs for the recursive space-time trellis modulation outperforms the group USTC used by Schlegel and Grant.
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Title: A Survey on Space-Time Turbo Codes

Section 1: INTRODUCTION
Description 1: Introduce space-time turbo codes (STT), their benefits, and the reasons for their current research interest.

Section 2: BACKGROUND STUDY
Description 2: Discuss the related work previously proposed in the literature for space-time turbo coding and present a review of foundational space-time coding techniques and their developments.

Section 3: FUTURE ENHANCEMENT
Description 3: Explain further improvements and future directions in the modeling and analysis of space-time coding schemes, including simulations and performance evaluations.

Section 4: CONCLUSION
Description 4: Provide a summary of space-time turbo codes, their key techniques, potential future enhancements, and the overall impact on wireless communication systems.