Sequential decoding

About: Sequential decoding is a research topic. Over the lifetime, 8667 publications have been published within this topic receiving 204271 citations.

Dynamics and performance analysis of analog iterative decoding for low-density parity-check (LDPC) codes

Abstract: Conventional iterative decoding with flooding or parallel schedule can be formulated as a fixed-point problem solved iteratively by a successive substitution (SS) method. In this paper, we investigate the dynamics of a continuous-time (asynchronous) analog implementation of iterative decoding, and show that it can be approximated as the application of the well-known successive relaxation (SR) method for solving the fixed-point problem. We observe that SR with the optimal relaxation factor can considerably improve the error-rate performance of iterative decoding for short low-density parity-check (LDPC) codes, compared with SS. Our simulation results for the application of SR to belief propagation (sum-product) and min-sum algorithms demonstrate improvements of up to about 0.7 dB over the standard SS for randomly constructed LDPC codes. The improvement in performance increases with the maximum number of iterations, and by accordingly reducing the relaxation factor. The asymptotic result, corresponding to an infinite maximum number of iterations and infinitesimal relaxation factor, represents the steady-state performance of analog iterative decoding. This means that under ideal circumstances, continuous-time (asynchronous) analog decoders can outperform their discrete-time (synchronous) digital counterparts by a large margin. Our results also indicate that with the assumption of a truncated Gaussian distribution for the random delays among computational modules, the error-rate performance of the analog decoder, particularly in steady state, is rather independent of the variance of the distribution. The proposed simple model for analog decoding, and the associated performance curves, can be used as an "ideal analog decoder" benchmark for performance evaluation of analog decoding circuits.

Performance of Reed-Solomon block turbo code

Abstract: Thanks to recent progress in the iterative decoding of concatenated codes, several new fields of investigation have appeared. In this paper, we present a first approach of the iterative decoding of Reed-Solomon (RS) product codes: "Turbo codes RS". Two methods to construct RS product codes are given. The iterative decoding of the RS product codes is based on the soft decoding and the soft decision of the component codes. The performance of RS turbo codes have been evaluated on the Gaussian and Rayleigh channels using Monte Carlo simulation. Coding gains up to 5.5 dB for a BER (bit error rate) of 10/sup -5/ have been obtained on the Gaussian channel. This new coding scheme is very attractive for data storage applications where the RS product codes are often used.

Message passing algorithms and improved LP decoding

Abstract: Linear programming decoding for low-density parity check codes (and related domains such as compressed sensing) has received increased attention over recent years because of its practical performance --coming close to that of iterative decoding algorithms--- and its amenability to finite-blocklength analysis. Several works starting with the work of Feldman et al. showed how to analyze LP decoding using properties of expander graphs. This line of analysis works for only low error rates, about a couple of orders of magnitude lower than the empirically observed performance. It is possible to do better for the case of random noise, as shown by Daskalakis et al. and Koetter and Vontobel. Building on work of Koetter and Vontobel, we obtain a novel understanding of LP decoding, which allows us to establish a 0.05-fraction of correctable errors for rate-1/2 codes; this comes very close to the performance of iterative decoders and is significantly higher than the best previously noted correctable bit error rate for LP decoding. Unlike other techniques, our analysis directly works with the primal linear program and exploits an explicit connection between LP decoding and message passing algorithms.An interesting byproduct of our method is a notion of a "locally optimal" solution that we show to always be globally optimal (i.e., it is the nearest codeword). Such a solution can in fact be found in near-linear time by a "re-weighted" version of the min-sum algorithm, obviating the need for linear programming. Our analysis implies, in particular, that this re-weighted version of the min-sum decoder corrects up to a 0.05-fraction of errors.

A Huffman-Shannon-Fano code

Abstract: A variable-word-length minimum-redundant code is described. It has the advantages of both the Huffman and Shannon-Fano codes in that it reduces transmission time, storage space, translation table space, and encoding and decoding times.

On optimal quasi-orthogonal space-time block codes with minimum decoding complexity

Abstract: In this paper, we first present a necessary and sufficient condition on linear transformations for an QOSTBC to possess the minimum ML decoding complexity, i.e., real symbol pair-wise decoding. We then present optimal linear transformations of information symbols for quasi-orthogonal space-time block codes (QOSTBC) with minimum ML decoding complexity. The optimality is in the sense that the diversity product (or product distance) is maximized when the mean transmission power is fixed