Comparative Study of Turbo Decoding Techniques: An Overview
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paper_title: Interleaver design for turbo codes

paper_content:

A new type of interleaver for rate 1/2 turbo codes is designed which allows each information bit to be associated with its own coded bit. In this way the correction capability of the code is uniformly distributed over all information bits. This provides twice the performance over a block interleaver.
---
paper_title: Iterative decoding of binary block and convolutional codes

paper_content:

Iterative decoding of two-dimensional systematic convolutional codes has been termed "turbo" (de)coding. Using log-likelihood algebra, we show that any decoder can be used which accepts soft inputs-including a priori values-and delivers soft outputs that can be split into three terms: the soft channel and a priori inputs, and the extrinsic value. The extrinsic value is used as an a priori value for the next iteration. Decoding algorithms in the log-likelihood domain are given not only for convolutional codes but also for any linear binary systematic block code. The iteration is controlled by a stop criterion derived from cross entropy, which results in a minimal number of iterations. Optimal and suboptimal decoders with reduced complexity are presented. Simulation results show that very simple component codes are sufficient, block codes are appropriate for high rates and convolutional codes for lower rates less than 2/3. Any combination of block and convolutional component codes is possible. Several interleaving techniques are described. At a bit error rate (BER) of 10/sup -4/ the performance is slightly above or around the bounds given by the cutoff rate for reasonably simple block/convolutional component codes, interleaver sizes less than 1000 and for three to six iterations.
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paper_title: Power and Bandwidth Efficient Digital Communication Using Turbo Codes in Multilevel Codes

paper_content:

The recently proposed Turbo codes are applied to bandwidth efficient modulation schemes via multilevel coding. For this purpose, Turbo codes are extended for a wide range of fine tunable rates by puncturing. A straightforward derivation of iterative Turbo decoding and the concept of extrinsic information is presented. New design rules for multilevel codes with arbitrary component codes and codeword lengths are derived from information theory. Simulation results show that application of Turbo codes to properly designed multilevel coding schemes leads to digital transmission schemes with high power and bandwidth efficiency.
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paper_title: Application of turbo-codes to a CDMA mobile radio system using joint detection and antenna diversity

paper_content:

In order to guarantee communication links of sufficient quality, channel coding is required in mobile radio systems. A novel class of binary parallel concatenated recursive systematic convolutional codes termed turbo-codes allowing a near Shannon limit performance without affecting the data rate was proposed and investigated for additive white Gaussian noise channels. Using a simple turbo-code based on a 16-state recursive systematic convolutional code, the authors demonstrate the applicability of turbo-codes to a CDMA mobile radio system using joint detection and coherent receiver antenna diversity. The considered turbo-code is tailored to the delay requirements of voice communications. Furthermore, the performance advantage of this turbo-code over a regular convolutional code is demonstrated. >
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paper_title: Comparison of turbo-code decoders applied to short frame transmission systems

paper_content:

A novel class of binary parallel concatenated recursive systematic convolutional codes termed turbo-codes, having amazing error correcting capabilities, has previously been proposed. However, the decoding of turbo-codes relies on the application of soft input/soft output decoders. Such decoders can be realized either using maximum a posteriori (MAP) symbol estimators or MAP sequence estimators, e.g., the a priori soft output Viterbi algorithm (APRI-SOVA). In this paper, the structure of turbo-code encoders as well as of turbo-code decoders is described. In particular, four different decoder structures are illustratively characterized and their error rate performance capabilities compared in both additive white Gaussian noise (AWGN) as well as flat Rayleigh-fading channels based on extensive simulation results for short frames used for speech transmission in the uplink of a digital mobile radio system applying code division multiple access and joint detection. The decoders are investigated as follows: 1) the MAP symbol estimator-based approach used by Berrou et al. [1993], 2) the MAP symbol estimator-based approach used by Robertson [1994], 3) a new reduced complexity MAP symbol estimator-based approach [Jung 1995], and 4) an APRI-SOVA based approach used by Hagenauer et al. [1994].
---
paper_title: Design of Parallel Concatenated Convolutional Codes

paper_content:

A parallel concatenated convolutional coding scheme consists of two constituent systematic: convolutional encoders linked by an interleaver. The information bits at the input of the first encoder are scrambled by the interleaver before entering the second encoder. The codewords of the parallel concatenated code consist of the information bits followed by the parity check bits of both encoders. Parallel concatenated codes (turbo codes), decoded through an iterative decoding algorithm of relatively low complexity, have been shown to yield remarkable coding gains close to theoretical limits. We characterize the separate contributions that the interleaver length and constituent codes give to the overall performance of the parallel concatenated code, and present some guidelines for the optimal design of the constituent convolutional codes.
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paper_title: Bandwidth-efficient turbo trellis-coded modulation using punctured component codes

paper_content:

We present a bandwidth-efficient channel coding scheme that has an overall structure similar to binary turbo codes, but employs trellis-coded modulation (TCM) codes (including multidimensional codes) as component codes. The combination of turbo codes with powerful bandwidth-efficient component codes leads to a straightforward encoder structure, and allows iterative decoding in analogy to the binary turbo decoder. However, certain special conditions may need to be met at the encoder, and the iterative decoder needs to be adapted to the decoding of the component TCM codes. The scheme has been investigated for 8-PSK, 16-QAM, and 64-QAM modulation schemes with varying overall bandwidth efficiencies. A simple code choice based on the minimal distance of the punctured component code has also been performed. The interset distances of the partitioning tree can be used to fix the number of coded and uncoded bits. We derive the symbol-by-symbol MAP component decoder operating in the log domain, and apply methods of reducing decoder complexity. Simulation results are presented and compare the scheme with traditional TCM as well as turbo codes with Gray mapping. The results show that the novel scheme is very powerful, yet of modest complexity since simple component codes are used.
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paper_title: Unveiling turbo codes: some results on parallel concatenated coding schemes

paper_content:

A parallel concatenated coding scheme consists of two simple constituent systematic encoders linked by an interleaver. The input bits to the first encoder are scrambled by the interleaver before entering the second encoder. The codeword of the parallel concatenated code consists of the input bits to the first encoder followed by the parity check bits of both encoders. This construction can be generalized to any number of constituent codes. Parallel concatenated schemes employing two convolutional codes as constituent codes, in connection with an iterative decoding algorithm of complexity comparable to that of the constituent codes, have been previously shown to yield remarkable coding gains close to theoretical limits. They have been named, and are known as, "turbo codes". We propose a method to evaluate an upper bound to the bit error probability of a parallel concatenated coding scheme averaged over all interleavers of a given length. The analytical bounding technique is then used to shed some light on some crucial questions, which have been floating around in the communications community since the proposal of turbo codes.
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paper_title: A distance spectrum interpretation of turbo codes

paper_content:

The performance of turbo codes is addressed by examining the code's distance spectrum. The "error floor" that occurs at moderate signal-to-noise ratios is shown to be a consequence of the relatively low free distance of the code. It is also shown that the "error floor" can be lowered by increasing the size of the interleaver without changing the free distance of the code. Alternatively, the free distance of the code may be increased by using primitive feedback polynomials. The excellent performance of turbo codes at low signal-to-noise ratios is explained in terms of the distance spectrum. The interleaver in the turbo encoder is shown to reduce the number of low-weight codewords through a process called "spectral thinning." This thinned distance spectrum results in the free distance asymptote being the dominant performance parameter for low and moderate signal-to-noise ratios.
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paper_title: Turbo-codes and high spectral efficiency modulation

paper_content:

This paper presents a new coding scheme based on the association of a turbo-code with a bandwith efficient modulation. It is shown that the new coding scheme provides a substantial coding gain both on Gaussian channels and Rayleigh channels. On a Gaussian channel, it outperforms 64-state trellis-coded modulation (TCM) by 2.5 dB at the bit error rate (BER) of 10/sup -6/. On a Rayleigh fading channel, it outperforms 64-state TCM optimized for that environment. >
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paper_title: Optimal decoding of linear codes for minimizing symbol error rate

paper_content:

A process for the preparation by sintering of molybdenum based alloys containing at least one reinforcing element, characterized in that at least one addition compound is introduced in the liquid state into molybdenum used in the form of at least one of the members belonging to the group consisting of the salts of molybdenum, the oxides of molybdenum and metallic molybdenum, and in that carbon is then added in sufficient quantity and the intimate member, after reduction of the matrix to the metallic state of molybdenum was used in the form of at least one molybdenum salt or at least one molybdenum oxide, is sintered at a temperature at which the said carbon at least partially reduces the addition compound.
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paper_title: A Viterbi algorithm with soft-decision outputs and its applications

paper_content:

The Viterbi algorithm (VA) is modified to deliver the most likely path sequence in a finite-state Markov chain, as well as either the a posteriori probability for each bit or a reliability value. With this reliability indicator the modified VA produces soft decisions to be used in the decoding of outer codes. The inner software output Viterbi algorithm (SOVA) accepts and delivers soft sample values and can be regraded as a device for improving the signal-to-noise ratio, similar to an FM demodulator. Several applications are investigated to show the gain over the conventional hard-deciding VA, including concatenated convolutional codes, concatenation of trellis-coded modulation with convolutional FEC (forward error correcting) codes, and coded Viterbi equalization. For these applications additional gains of 1-4 dB as compared to the classical hard-deciding algorithms were found. For comparison, the more complex symbol-to-symbol MAP, whose optimal a posteriori probabilities can be transformed into soft outputs, was investigated. >
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paper_title: Optimal decoding of linear codes for minimizing symbol error rate

paper_content:

A process for the preparation by sintering of molybdenum based alloys containing at least one reinforcing element, characterized in that at least one addition compound is introduced in the liquid state into molybdenum used in the form of at least one of the members belonging to the group consisting of the salts of molybdenum, the oxides of molybdenum and metallic molybdenum, and in that carbon is then added in sufficient quantity and the intimate member, after reduction of the matrix to the metallic state of molybdenum was used in the form of at least one molybdenum salt or at least one molybdenum oxide, is sintered at a temperature at which the said carbon at least partially reduces the addition compound.
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paper_title: The viterbi algorithm

paper_content:

The Viterbi algorithm (VA) is a recursive optimal solution to the problem of estimating the state sequence of a discrete-time finite-state Markov process observed in memoryless noise. Many problems in areas such as digital communications can be cast in this form. This paper gives a tutorial exposition of the algorithm and of how it is implemented and analyzed. Applications to date are reviewed. Increasing use of the algorithm in a widening variety of areas is foreseen.
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paper_title: The Super-Trellis Structure of Turbo Codes

paper_content:

In this contribution we derive the super-trellis structure of turbo codes. We show that this structure and its associated decoding complexity depend strongly on the interleaver applied in the turbo encoder. We provide upper bounds for the super-trellis complexity. Turbo codes are usually decoded by an iterative decoding algorithm, which is suboptimum. Applying the super-trellis structure, we can optimally decode simple turbo codes and compare the associated bit-error rate results to those of iterative algorithms.
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paper_title: Approaching Shannon's capacity limit by 0.2 dB using simple Hamming codes

paper_content:

The authors show that the Shannon capacity limit for the additive white Gaussian noise (AWGN) channel can be approached within 0.27 dB at a bit error rate (BER) of 10/sup -5/ by applying long but simple Hamming codes as component codes to an iterative turbo-decoding scheme. In general, the complexity of soft-in/soft-out decoding of binary block codes is rather high. However, the application of a neurocomputer in combination with a parallelization of the decoding rule facilitates an implementation of the decoding algorithm in the logarithmic domain which requires only matrix additions and multiplications. But the storage requirement might still be quite high depending on the interleavers used.
---
paper_title: A Viterbi algorithm with soft-decision outputs and its applications

paper_content:

The Viterbi algorithm (VA) is modified to deliver the most likely path sequence in a finite-state Markov chain, as well as either the a posteriori probability for each bit or a reliability value. With this reliability indicator the modified VA produces soft decisions to be used in the decoding of outer codes. The inner software output Viterbi algorithm (SOVA) accepts and delivers soft sample values and can be regraded as a device for improving the signal-to-noise ratio, similar to an FM demodulator. Several applications are investigated to show the gain over the conventional hard-deciding VA, including concatenated convolutional codes, concatenation of trellis-coded modulation with convolutional FEC (forward error correcting) codes, and coded Viterbi equalization. For these applications additional gains of 1-4 dB as compared to the classical hard-deciding algorithms were found. For comparison, the more complex symbol-to-symbol MAP, whose optimal a posteriori probabilities can be transformed into soft outputs, was investigated. >
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paper_title: An Intuitive Justification and a Simplified Implementation of the MAP Decoder for Convolutional Codes

paper_content:

An intuitive shortcut to understanding the maximum a posteriori (MAP) decoder is presented based on an approximation. This is shown to correspond to a dual-maxima computation combined with forward and backward recursions of Viterbi algorithm computations. The logarithmic version of the MAP algorithm can similarly be reduced to the same form by applying the same approximation. Conversely, if a correction term is added to the approximation, the exact MAP algorithm is recovered. It is also shown how the MAP decoder memory can be drastically reduced at the cost of a modest increase in processing speed.
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paper_title: Approaching the Shannon Limit: theorist's dream and practitioner's challenge

paper_content:

Nearly half a century after Shannon established the channel capacity of a noisy channel as the insurmountable limit on the rate of reliable communication, a combination of long known but dormant concepts and a fresh approach has brought us to within a remarkably small distance of that limit. For an additive white Gaussian (AWGN) channel, low error probabilities have been achieved at rates greater than eighty percent of capacity, or in terms of bit energy-to-noise density ratio, E/sub b//N/sub 0/ within less than 1dB of the minimum value which corresponds to operation at channel capacity.
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paper_title: Source-controlled channel decoding

paper_content:

The performance of a channel decoder can be considerably improved if a priori information about the source bits is used. Many source coding schemes for analog signals still have correlation between bits of successive frames. We show that soft-outputs and bit correlations can be converted into a priori values for the next frame and used by a modified Viterbi algorithm, the APRI-SOVA. Gains of several decibels with respect to classical Viterbi decoding are obtained for the mobile GSM coding scheme and PCM transmission schemes. >
---
paper_title: A Viterbi algorithm with soft-decision outputs and its applications

paper_content:

The Viterbi algorithm (VA) is modified to deliver the most likely path sequence in a finite-state Markov chain, as well as either the a posteriori probability for each bit or a reliability value. With this reliability indicator the modified VA produces soft decisions to be used in the decoding of outer codes. The inner software output Viterbi algorithm (SOVA) accepts and delivers soft sample values and can be regraded as a device for improving the signal-to-noise ratio, similar to an FM demodulator. Several applications are investigated to show the gain over the conventional hard-deciding VA, including concatenated convolutional codes, concatenation of trellis-coded modulation with convolutional FEC (forward error correcting) codes, and coded Viterbi equalization. For these applications additional gains of 1-4 dB as compared to the classical hard-deciding algorithms were found. For comparison, the more complex symbol-to-symbol MAP, whose optimal a posteriori probabilities can be transformed into soft outputs, was investigated. >
---
paper_title: Source-controlled channel decoding

paper_content:

The performance of a channel decoder can be considerably improved if a priori information about the source bits is used. Many source coding schemes for analog signals still have correlation between bits of successive frames. We show that soft-outputs and bit correlations can be converted into a priori values for the next frame and used by a modified Viterbi algorithm, the APRI-SOVA. Gains of several decibels with respect to classical Viterbi decoding are obtained for the mobile GSM coding scheme and PCM transmission schemes. >
---
paper_title: A Viterbi algorithm with soft-decision outputs and its applications

paper_content:

The Viterbi algorithm (VA) is modified to deliver the most likely path sequence in a finite-state Markov chain, as well as either the a posteriori probability for each bit or a reliability value. With this reliability indicator the modified VA produces soft decisions to be used in the decoding of outer codes. The inner software output Viterbi algorithm (SOVA) accepts and delivers soft sample values and can be regraded as a device for improving the signal-to-noise ratio, similar to an FM demodulator. Several applications are investigated to show the gain over the conventional hard-deciding VA, including concatenated convolutional codes, concatenation of trellis-coded modulation with convolutional FEC (forward error correcting) codes, and coded Viterbi equalization. For these applications additional gains of 1-4 dB as compared to the classical hard-deciding algorithms were found. For comparison, the more complex symbol-to-symbol MAP, whose optimal a posteriori probabilities can be transformed into soft outputs, was investigated. >
---
paper_title: Interleaver design for turbo codes

paper_content:

A new type of interleaver for rate 1/2 turbo codes is designed which allows each information bit to be associated with its own coded bit. In this way the correction capability of the code is uniformly distributed over all information bits. This provides twice the performance over a block interleaver.
---
paper_title: Interleaver design for turbo codes

paper_content:

A new type of interleaver for rate 1/2 turbo codes is designed which allows each information bit to be associated with its own coded bit. In this way the correction capability of the code is uniformly distributed over all information bits. This provides twice the performance over a block interleaver.
---
paper_title: Turbo-coded Orthogonal Frequency Division Multiplex transmission of 8 kbps encoded speech

paper_content:

In this paper we have considered using turbo channel coding to encode the 8 kbits/s output from the G.729 speech codec. The source and channel coded bits are then transmitted using a wideband Orthogonal Frequency Division Multiplexing (OFDM) system in the framework of the Mode-I FRAMES proposals [I]. We illustrate the benefits of using OFDM with channel coding to alleviate some of the problems associated with wideband fading channels. Furthermore, we discuss how OFDM can be used in conjunction with the G.729 speech codec and half rate channel coding in order to utilise one speechldata FRAMES subbburst. Finally some of the issues and problems associated with using turbo coded OFDM in speech transmission systems are considered using the system characterised in Table 1. In Figure 6 a channel SNR of 6dB appears sufficiently high under the stipulated system conditions for near-unimpaired speech transmission.
---
paper_title: Iterative decoding of binary block and convolutional codes

paper_content:

Iterative decoding of two-dimensional systematic convolutional codes has been termed "turbo" (de)coding. Using log-likelihood algebra, we show that any decoder can be used which accepts soft inputs-including a priori values-and delivers soft outputs that can be split into three terms: the soft channel and a priori inputs, and the extrinsic value. The extrinsic value is used as an a priori value for the next iteration. Decoding algorithms in the log-likelihood domain are given not only for convolutional codes but also for any linear binary systematic block code. The iteration is controlled by a stop criterion derived from cross entropy, which results in a minimal number of iterations. Optimal and suboptimal decoders with reduced complexity are presented. Simulation results show that very simple component codes are sufficient, block codes are appropriate for high rates and convolutional codes for lower rates less than 2/3. Any combination of block and convolutional component codes is possible. Several interleaving techniques are described. At a bit error rate (BER) of 10/sup -4/ the performance is slightly above or around the bounds given by the cutoff rate for reasonably simple block/convolutional component codes, interleaver sizes less than 1000 and for three to six iterations.
---
paper_title: Comparison of turbo-code decoders applied to short frame transmission systems

paper_content:

A novel class of binary parallel concatenated recursive systematic convolutional codes termed turbo-codes, having amazing error correcting capabilities, has previously been proposed. However, the decoding of turbo-codes relies on the application of soft input/soft output decoders. Such decoders can be realized either using maximum a posteriori (MAP) symbol estimators or MAP sequence estimators, e.g., the a priori soft output Viterbi algorithm (APRI-SOVA). In this paper, the structure of turbo-code encoders as well as of turbo-code decoders is described. In particular, four different decoder structures are illustratively characterized and their error rate performance capabilities compared in both additive white Gaussian noise (AWGN) as well as flat Rayleigh-fading channels based on extensive simulation results for short frames used for speech transmission in the uplink of a digital mobile radio system applying code division multiple access and joint detection. The decoders are investigated as follows: 1) the MAP symbol estimator-based approach used by Berrou et al. [1993], 2) the MAP symbol estimator-based approach used by Robertson [1994], 3) a new reduced complexity MAP symbol estimator-based approach [Jung 1995], and 4) an APRI-SOVA based approach used by Hagenauer et al. [1994].
---
paper_title: Interleaver design for turbo codes

paper_content:

A new type of interleaver for rate 1/2 turbo codes is designed which allows each information bit to be associated with its own coded bit. In this way the correction capability of the code is uniformly distributed over all information bits. This provides twice the performance over a block interleaver.
---
paper_title: Multilevel turbo coding with short interleavers

paper_content:

The impact of the interleaver, embedded in the encoder for a parallel concatenated code, called the turbo code, is studied. The known turbo codes consist of long random interleavers, whose purpose is to reduce the value of the error coefficients. It is shown that an increased minimum Hamming distance can be obtained by using a structured interleaver. For low bit-error rates (BERs), we show that the performance of turbo codes with a structured interleaver is better than that obtained with a random interleaver. Another important advantage of the structured interleaver is the short length required, which yields a short decoding delay and reduced decoding complexity (in terms of memory). We also consider the use of turbo codes as component codes in multilevel codes. Powerful coding structures that consist of two component codes are suggested. Computer simulations are performed in order to evaluate the reduction in coding gain due to suboptimal iterative decoding. From the results of these simulations we deduce that the degradation in the performance (due to suboptimal decoding) is very small.
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paper_title: Application of turbo-codes to a CDMA mobile radio system using joint detection and antenna diversity

paper_content:

In order to guarantee communication links of sufficient quality, channel coding is required in mobile radio systems. A novel class of binary parallel concatenated recursive systematic convolutional codes termed turbo-codes allowing a near Shannon limit performance without affecting the data rate was proposed and investigated for additive white Gaussian noise channels. Using a simple turbo-code based on a 16-state recursive systematic convolutional code, the authors demonstrate the applicability of turbo-codes to a CDMA mobile radio system using joint detection and coherent receiver antenna diversity. The considered turbo-code is tailored to the delay requirements of voice communications. Furthermore, the performance advantage of this turbo-code over a regular convolutional code is demonstrated. >
---
paper_title: Comparison of turbo-code decoders applied to short frame transmission systems

paper_content:

A novel class of binary parallel concatenated recursive systematic convolutional codes termed turbo-codes, having amazing error correcting capabilities, has previously been proposed. However, the decoding of turbo-codes relies on the application of soft input/soft output decoders. Such decoders can be realized either using maximum a posteriori (MAP) symbol estimators or MAP sequence estimators, e.g., the a priori soft output Viterbi algorithm (APRI-SOVA). In this paper, the structure of turbo-code encoders as well as of turbo-code decoders is described. In particular, four different decoder structures are illustratively characterized and their error rate performance capabilities compared in both additive white Gaussian noise (AWGN) as well as flat Rayleigh-fading channels based on extensive simulation results for short frames used for speech transmission in the uplink of a digital mobile radio system applying code division multiple access and joint detection. The decoders are investigated as follows: 1) the MAP symbol estimator-based approach used by Berrou et al. [1993], 2) the MAP symbol estimator-based approach used by Robertson [1994], 3) a new reduced complexity MAP symbol estimator-based approach [Jung 1995], and 4) an APRI-SOVA based approach used by Hagenauer et al. [1994].
---
paper_title: Illuminating the structure of code and decoder of parallel concatenated recursive systematic (turbo) codes

paper_content:

A coding scheme (turbo codes) was proposed, that achieves almost reliable data communication at signal-to-noise ratios very close to the Shannon-limit. We show that the associated iterative decoder can be formulated in a simpler fashion by passing information from one decoder to the next using log-likelihood ratios as opposed to channel values that need to be normalized. Also no heuristically determined correction parameters are necessary for stable decoding. In addition, we can reduce the average number of iterations needed for the same BER performance by determining when further iterations achieve no more benefit. Furthermore, it seems that the trellis-termination problem appears non-trivial and we give a pragmatic suboptimal solution. We investigate different block sizes and also a hybrid scheme that performs extremely well with less computations. A drawback of the codes has been discovered: the BER curves show a flattening at higher signal-to-noise ratios, this is due to the small minimum distance of the whole code. By analyzing the interleaver used in the encoder we can calculate approximations to the BER at high SNRs. Finally, by careful interleaver manipulation the minimum distance of the code can be increased and the error-coefficient for the remaining small distance events can be further reduced. Furthermore, we have investigated the influence of the interleaver length on the SNR needed to achieve a certain BER. Simulations confirm both the analytical approximation to the BER as well as the method for interleaver design which yields a marked improvement at higher SNR.
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paper_title: Results on turbo-codes for speech transmission in a joint detection CDMA mobile radio system with coherent receiver antenna diversity

paper_content:

Turbo-codes which are applicable to speech transmission in digital mobile radio systems are treated. Three turbo-codes of different complexity are presented. The proposed turbo-codes are suitable for the application to speech transmission in the joint detection code-division multiple access (JD-CDMA) mobile radio system with coherent receiver antenna diversity (CRAD) which are described concisely. The performance of the designed turbo-codes in terms of bit and frame error rates are shown in the case of additive white Gaussian noise (AWGN) channels, flat Rayleigh fading channels, and in the uplink of the aforementioned JD-CDMA mobile radio system.
---
paper_title: Interleaver design for turbo codes

paper_content:

A new type of interleaver for rate 1/2 turbo codes is designed which allows each information bit to be associated with its own coded bit. In this way the correction capability of the code is uniformly distributed over all information bits. This provides twice the performance over a block interleaver.
---
paper_title: Burst-by-burst adaptive wideband wireless video telephony

paper_content:

The design trade-offs of interactive wireless video systems are discussed and performance comparisons are provided both in the context of second- and third-generation wireless videophone systems. We commence our discussions by a comparative study of arbitrarily programmable, but fixed-rate, videophone codecs using quarter common intermediate format (QCIF) video sequences scanned at 10 frames/s. These proprietary codecs were designed to allow direct replacement of mobile radio voice codecs in second generation wireless systems, such as the Pan-European GSM, the American IS-54 and IS-95 as well as the Japanese systems, operating at 13, 8, 9.6 and 6.7 kbps, respectively, although better video quality is maintained over higher-rate, 32 kbps cordless systems, such as the Japanese PHS and the European DECT and CT2 systems. From the range of codecs investigated, best overall performance was achieved by our vector-quantised codecs, followed by the discrete cosine transformed and the quadtree-based schemes. The associated video peak signal-to-noise ratio (PSNR) was around 30 dB, while the subjective video quality can be assessed under http://www-mobile.ecs.soton.ac.uk. A range of multimode wireless transceivers is also proposed. The second part of the paper is dedicated to burst-by-burst (BbB) adaptive wireless video transceivers employing the standard H.263 codec. It is demonstrated that the proposed BbB adaptive transceivers provide an improved video performance in comparison to their statically reconfigured counterparts in the context of both wideband BbB adaptive quadrature amplitude modulation (AQAM) transceivers and the joint-detection based code division multiple access (CDMA) transceivers of the third generation systems.
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paper_title: Adaptive multicarrier modulation: a convenient framework for time-frequency processing in wireless communications

paper_content:

A historical perspective of orthogonal frequency-division multiplexing (OFDM) is given with reference to its literature. Its advantages and disadvantages are reviewed, and its performance is characterized over highly dispersive channels. The effects of both time- and frequency-domain synchronization errors are quantified, and a range of solutions proposed in the recent literature are reviewed. One of the main objectives of this review is to highlight the recent thinking behind adaptive bit allocation and turbo coding in the context of OFDM. This paper concludes with a wide-ranging throughput comparison of the schemes discussed herein under the unified constraint of a fixed target bit error rate of 10/sup -4/.
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paper_title: A turbo-coded burst-by-burst adaptive wide-band speech transceiver

paper_content:

Turbo-coded burst-by-burst adaptive orthogonal frequency division multiplex (AOFDM) wide-band speech transceivers are proposed. A constant throughput adaptive OFDM transceiver was designed and benchmarked against a time-variant rate scheme. The proposed joint adaptation of source-codec, channel-codec, and modulation regime results in at- tractive, robust, high-quality audio systems, capable of conveying near-unimpaired wide-band audio signals over fading dispersive channels for signal-to-noise ratios (SNR) in excess of about 5 dB. Index Terms—Adaptive OFDM, audio compression, transmis- sion, wide-band speech compression.
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paper_title: Subband-adaptive turbo-coded OFDM-based interactive video telephony

paper_content:

A range of adaptive orthogonal frequency division multiplex (AOFDM) video systems are proposed for interactive communications over wireless channels. The proposed constant target bit-rate subband-adaptive OFDM modems can provide a lower bit error rate than a corresponding conventional OFDM modem. The slightly more complex switched or time-variant target bit rate AOFDM modems can provide a balanced video quality performance, across a wider range of channel signal-to-noise ratios, maintaining the best video performance. Upon invoking the technique advocated, irrespective of the channel conditions experienced, the transceiver achieves always the best possible video quality by automatically adjusting the achievable bit rate and the associated video quality in order to match the channel quality experienced. This is achieved on a near-instantaneous basis under given propagation conditions in order to cater for the effects of path-loss, fast-fading, slow-fading, dispersion, etc. Furthermore, when the mobile is roaming in a hostile outdoor propagation environment, typically low-order, low-rate modem modes are invoked, while in benign indoor environments predominantly the high-rate, high source-signal representation quality modes are employed.
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paper_title: The Super-Trellis Structure of Turbo Codes

paper_content:

In this contribution we derive the super-trellis structure of turbo codes. We show that this structure and its associated decoding complexity depend strongly on the interleaver applied in the turbo encoder. We provide upper bounds for the super-trellis complexity. Turbo codes are usually decoded by an iterative decoding algorithm, which is suboptimum. Applying the super-trellis structure, we can optimally decode simple turbo codes and compare the associated bit-error rate results to those of iterative algorithms.
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paper_title: OFDM-based turbo-coded hierarchical and non-hierarchical terrestrial mobile digital video broadcasting

paper_content:

The feasibility of terrestrial digital video broadcast (DVB) to mobile receivers is studied and turbo coded performance enhancements are proposed. Initially, the MPEG-2 codec is subjected to a rigorous bit error sensitivity investigation, in order to assist in designing various error protection schemes for wireless DVB transmission. The turbo codec is shown to provide signal-to-noise ratio (SNR) performance advantages in excess of 5-6 dB over conventional convolutional coding both in terms of bit error rate and video quality. Our experiments suggested that-despite our expectations-multi-class data partitioning did not result in error resilience improvements, since a high proportion of relatively sensitive video bits had to be relegated to the lower integrity subchannel, when invoking a powerful low-rate channel codec in the high-integrity protection class. Nonetheless, DVB transmission to mobile receivers is feasible, when using turbo-coded OFDM transceivers at realistic power-budget requirements under the investigated highly dispersive fading channel conditions. It is interesting to note furthermore that the 5-6 dB SNR improvement due to turbo coding allows us to invoke for example the double-throughput 16-level quadrature amplitude modulation (16-QAM) mode instead of the standard convolutional-coded 4-QAM mode. This facilitates doubling the bit rate and hence improving the video quality.
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paper_title: Satellite based turbo-coded, blind-equalized 4-QAM and 16-QAM digital video broadcasting

paper_content:

The pan-European digital satellite video broadcasting (DVB-S) system's performance is characterized and improved with the aid of turbo coding and multi-level modulation. Specifically, various configurations of blind equalizers and convolutional as well as turbo codecs operating at different code rates were investigated. The standard system's performance was improved upon replacing the conventional convolutional codec by a turbo codec. Lastly, the feasibility of employing blind equalized 16-level modulation within the DVB-S system is demonstrated, potentially doubling the available bit rate and hence improving the associated video quality at the cost of a higher signal-to-noise ratio (SNR) requirement. This extra transmitted power requirement can be eliminated upon invoking the more complex turbo codec, which requires lower transmitted power for attaining the same performance as the standard convolutional codes.
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paper_title: Interactive cellular and cordless video telephony: State-of-the-art system design principles and expected performance

paper_content:

Second-generation (2G) mobile radio standards have not been designed with video communications in mind, although the employment of error-resilient, constant-bit-rate proprietary video codecs over these systems is realistic. The third-generation (3G) systems are capable of providing higher rates and better communications integrity in support of video applications. This paper advocates the employment of burst-by-burst adaptive transceivers, which are capable of accommodating the time-variant channel quality fluctuation of wireless channels. This paper is concluded with a range of performance figures and system design guidelines for wireless systems.
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Title: Comparative Study of Turbo Decoding Techniques: An Overview

Section 1: Iterative Decoder Structure
Description 1: Write about the general structure of the iterative turbo decoder, including the components, their inputs and outputs, and the iterative process used in decoding.

Section 2: Introduction and Mathematical Preliminaries
Description 2: Discuss the basics of the MAP algorithm, including its historical background, mathematical formulation, and initial applications. Describe the concepts of a-posteriori probability, recursive calculations, and the use of Bayes' rule.

Section 3: Turbo Decoding Mathematical Preliminaries
Description 3: Explain the concepts of extrinsic and intrinsic information in turbo decoding, including how these are utilized in iterative decoding schemes.

Section 4: Iterative Turbo Decoding
Description 4: Describe the steps involved in iterative turbo decoding, detailing the operations of the component decoders, information exchange, and improvement in bit error rate (BER) with iterations.

Section 5: Introduction to Simplified Algorithms
Description 5: Provide an overview of simplified versions of the MAP algorithm, including the principles behind Max-Log-MAP and Log-MAP algorithms, their mathematical descriptions, and their applications in turbo coding.

Section 6: Mathematical Description of the SOVA Algorithm
Description 6: Delve into the Soft-Output Viterbi Algorithm (SOVA), its derivation, implementation, and how it differs from other turbo decoding algorithms in terms of complexity and performance.

Section 7: Turbo Decoding Example
Description 7: Use a numerical example to illustrate the iterative turbo decoding process using the SOVA algorithm. Describe the encoding and decoding steps, trellis representation, and computation of Log-Likelihood Ratios (LLRs).

Section 8: Comparison of the Component Decoder Algorithms
Description 8: Summarize the operations of various component decoders (MAP, Log-MAP, Max-Log-MAP, and SOVA). Highlight their complexities, performance differences, and practical considerations.

Section 9: The Effect of Various Codec Parameters
Description 9: Present simulation results showing the impact of different codec parameters on turbo code performance. Discuss the effects of the decoding algorithm, number of iterations, frame length, interleaver design, and component code structure.

Section 10: Turbo Coding over Rayleigh Channels
Description 10: Characterize the performance of turbo codes over Rayleigh fading channels. Compare results for different frame lengths, interleaver designs, and decoding algorithms, considering both perfectly interleaved and correlated fading scenarios.

Section 11: Conclusion
Description 11: Summarize the key findings from the comparative study of turbo decoding techniques. Highlight the tradeoffs between complexity and performance, and suggest potential areas for future research and application.