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sequential decoding of trellis codes at high spectral efficiencies

IEEE TRANSACTIONS ON INFORMATION THEORY 1997年第6期43卷 2013-2019页

作者： Wang, FQ Costello, DJ UNIV NOTRE DAME DEPT ELECT ENGNNOTRE DAMEIN 46556

A probabilistic algorithm is used to construct large constraint length trellis codes at high spectral efficiencies for use with sequential decoding. Linear trellis codes for two- and four-dimensional constellations with constraint lengths up to 19 are obtained. These codes can achieve 180 degrees rotational invariance. To achieve full 90 degrees rotational invariance, nonlinear trellis codes for four-dimensional constellations with constraint Lengths up to 19 are obtained. In both cases it is shown that the channel cutoff rate bound can be achieved using constraint lengths between 16 and 19 with sequential decoding at a bit-error rate of 10(-5)-10(-6) and that 4.9-5.8 dB real coding gains can be achieved over uncoded systems with the same spectral efficiency.

关键词： cutoff rate sequential decoding trellis-coded modulation

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sequential decoding with trellis shaping

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IEEE TRANSACTIONS ON INFORMATION THEORY 1995年第6期41卷 2037-2040页

作者： Couturier, S Costello, DJ Wang, FQ UNIV NOTRE DAME DEPT ELECT ENGNNOTRE DAMEIN 46556

sequential decoding of the channel code in a trellis-coded modulation system with trellis shaping can be used to reduce the system complexity and to achieve high coding gain with large constraint-length codes. It is shown that almost all the shaping gain that can be achieved when Viterbi decoding is used for the channel code can also be achieved when sequential decoding is used for the channel code. It is also shown that the real shaping gain is a function of both the SNR and the spectral efficiency.

关键词： trellis-coded modulation sequential decoding trellis shaping

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sequential decoding of convolutional codes for Rayleigh fading channels

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WIRELESS PERSONAL COMMUNICATIONS 2002年第1期20卷 61-74页

作者： Orten, P Svensson, A Nera Res N-1375 Billingstad Norway Chalmers Univ Technol Dept Signals & Syst Commun Syst Grp SE-41296 Gothenburg Sweden

The performance of sequential decoding of long constraint length convolutional codes is evaluated for Rayleigh fading channels. sequential decoding is not practical below a certain theoretical signal-to-noise ratio, and these theoretical limits are calculated for a number of modulation methods and code rates. As an example, with BPSK modulation, soft decisions and code rate 1/2, the theoretical signal-to-noise ratio per information bit is 5.7 dB. Above this limit the bit error rate can be made arbitrarily small by increasing the constraint length at no significant complexity cost. Furthermore, it is shown that with carefully chosen quantization steps, 8 level uniform quantization gives a negligible loss also for sequential decoding on a Rayleigh fading channel. Simulation results using 8 level quantization correspond well with the theoretical performance bounds. Also, the performance on a correlated channel with finite interleaving has been obtained. With an interleaver depth of 50 x 50 and a normalized doppler frequency equal to 0.01 we are only 0.5 dB away from the performance with perfect interleaving. Finally, bit error rate results show this scheme to compete well with Turbo codes.

关键词： sequential decoding Rayleigh fading Fano algorithm Pareto exponent wireless communication quantization

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sequential-decoding BASED ON AN ERROR CRITERION

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IEEE TRANSACTIONS ON INFORMATION THEORY 1992年第3期38卷 987-1001页

作者： ANDERSON, JB Department of Electrical Computer and Systems Engineering Rensselaer Polytechnic Institute Troy NY USA

A new analysis of sequential decoding is presented that is based on the requirement that a set probability of error P(e) be achieved. The error criterion implies a bounded tree or trellis search region;the shape of this is calculated for the case of a binary symmetric channel with crossover probability p and random tree codes of rate R. Since the search region is finite at all combinations of p and R below capacity, there is no cut-off rate phenomenon for any P(e) > 0. We calculate the decoder delay (search depth), path storage size, and the number of algorithm steps for several methods of tree search. These include searches without backtracking and backtracking searches that are depth- and metric-first. The search depth of the non-backtracking decoders satisfies the Gallager reliability exponent for block codes. In average paths searched, the backtracking decoders are much more efficient, but all types require the same peak storage allocation. Comparisons are made to well-known algorithms;in order of efficiency from best to worst these are Fano-like algorithms, the stack algorithm, algorithms like the M-algorithm, and the Viterbi algorithm.

关键词： CHANNEL decoding DECODER ALGORITHMS sequential decoding

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sequential decoding of Multiple Sequences for Synchronization Errors

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IEEE TRANSACTIONS ON COMMUNICATIONS 2024年第11期72卷 6660-6676页

作者： Banerjee, Anisha Lenz, Andreas Wachter-Zeh, Antonia Tech Univ Munich Inst Commun Engn D-80333 Munich Germany

sequential decoding, commonly applied to substitution channels, is a sub-optimal alternative to Viterbi decoding with significantly reduced memory costs. This work describes and analyzes a sequential decoder for convolutional codes over channels prone to insertion, deletion, and substitution errors. Our decoder expands the code trellis by a new channel-state variable, called drift state, as proposed by Davey and MacKay. A suitable decoding metric on that trellis for sequential decoding is derived, generalizing the original Fano metric. The decoder is also extended to facilitate the simultaneous decoding of multiple received sequences that arise from a single transmitted sequence. Under low-noise environments, our decoding approach reduces the decoding complexity by multiple orders of magnitude compared to Viterbi's algorithm, albeit at slightly higher bit error rates. An analytical method to determine the computational cutoff rate is also suggested. This analysis is supported by numerical evaluations of bit error rates and computational complexity, compared to optimal Viterbi decoding.

关键词： decoding Measurement Convolutional codes Hidden Markov models Viterbi algorithm Vectors Symbols DNA storage insertion deletion substitution (IDS) channel sequential decoding convolutional codes

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sequential decoding of Short Length Binary Codes: Performance Versus Complexity

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IEEE COMMUNICATIONS LETTERS 2021年第10期25卷 3195-3198页

作者： Lian, Bo Kschischang, Frank R. Univ Toronto Edward S Rogers Sr Dept Elect & Comp Engn Toronto ON M5S 3G4 Canada

sequential decoding of short length binary codes for the additive white Gaussian noise channel is considered. A variant of the variable-bias term (VBT) metric is introduced, producing useful trade-offs between performance and computational complexity. Comparisons are made with tail-biting convolutional codes decoded with a wrap-around Viterbi algorithm (WAVA) and with polar codes under successive-cancellation list (SCL) decoding. It is found that sequential decoding with the improved VBT metric has a better performance-complexity tradeoff than tail-biting codes under WAVA decoding (except at low complexities) but a worse performance-complexity tradeoff than polar codes under SCL decoding (except at high complexities).

关键词： decoding Measurement Complexity theory Signal to noise ratio Maximum likelihood decoding Polar codes Convolutional codes decoding complexity short length codes sequential decoding stack algorithm variable bias-term metric polar codes

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sequential-decoding OF LOW-DENSITY PARITY-CHECK CODES BY ADAPTIVE REORDERING OF PARITY CHECKS

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IEEE TRANSACTIONS ON INFORMATION THEORY 1992年第6期38卷 1833-1839页

作者： RADOSAVLJEVIC, B ARIKAN, E HAJEK, B BILKENT UNIV DEPT ELECT ENGNANKARATURKEY UNIV ILLINOIS URBANAIL 61801

decoding algorithms are investigated in which unpruned codeword trees are generated from an ordered list of parity checks. The order is computed from the received message, and low-density parity-check codes are used to help control the growth of the tree. Simulation results are given for the binary erasure channel. They suggest that for small erasure probability, the method is computationally feasible at rates above the computational cutoff rate.

关键词： Low-density codes sequential decoding computational cutoff rate.

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sequential decoding of Polar Codes

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IEEE COMMUNICATIONS LETTERS 2014年第7期18卷 1127-1130页

作者： Miloslavkaya, V. Trifonov, P. St Petersburg State Polytech Univ Dept Distributed Comp & Networking St Petersburg 194021 Russia

The problem of efficient decoding of polar codes is considered. A low-complexity sequential soft decision decoding algorithm is proposed. It is based on the successive cancellation approach, and it employs most likely... 详细信息

关键词： Polar codes sequential decoding successive cancellation

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Application of Guessing to sequential decoding of Polarization-Adjusted Convolutional (PAC) Codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2023年第8期71卷 4425-4436页

作者： Moradi, Mohsen Bilkent Univ Dept Elect & Elect Engn TR-06800 Ankara Turkiye

Despite the extreme error-correction performance, the amount of computation of sequential decoding of the polarization-adjusted convolutional (PAC) codes is random. In sequential decoding of convolutional codes, the cutoff rate denotes the region between rates whose average computational complexity of decoding is finite and those which is infinite. In this paper, by benefiting from the polarization and guessing techniques, we prove that the required computation in sequential decoding of pre-transformed polar codes polarizes, and this polarization determines which set of bit positions within the rate profile may result in high computational complexity. Based on this, we propose a technique for taming the Reed-Muller (RM) rate-profile construction, and the performance results demonstrate that the error-correction performance of the PAC codes can achieve the theoretical bounds using the tamed-RM rate-profile construction and requires a significantly lower computational complexity than the RM rate-profile construction.

关键词： PAC codes sequential decoding Fano algorithm polar coding channel coding guessing cutoff rate

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Bounds on a probability for the heavy tailed distribution and the probability of deficient decoding in sequential decoding

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IEEE TRANSACTIONS ON INFORMATION THEORY 2005年第3期51卷 990-1002页

作者： Hashimoto, T Univ Electrocommun Dept Elect Engn Chofu Tokyo 182 Japan

Although sequential decoding of convolutional codes gives a very small decoding error probability, the overall reliability is limited by the probability P-G of deficient decoding, the term introduced by Jelinek to refer to decoding failures caused mainly by buffer overflow. The number of computational efforts in sequential decoding has the Pareto distribution and it is this "heavy tailed" distribution that characterizes P-G. The heavy tailed distribution appears in many fields and buffer overflow is a typical example of the behaviors in which the heavy tailed distribution plays an important role. In this paper, we give a new bound on a probability in the tail of the heavy tailed distribution and, using the bound, prove the long-standing conjecture on P-G, that is, P-G approximate to constant x 1/(sigma(rho) Nrho-1) for a large speed factor sigma of the decoder and for a large receive buffer size N whenever the coding rate R and rho satisfy E(rho) = rhoR for 0 less than or equal to p less than or equal to 1.

关键词： buffer overflow convolutional code Fano algorithm heavy tailed distribution Pareto distribution probability of deficient decoding sequential decoding

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