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Sequential decoding
About: Sequential decoding is a research topic. Over the lifetime, 8667 publications have been published within this topic receiving 204271 citations.
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TL;DR: The analysis shows further that the "natural" choice of bias in the metric is the code rate and gives insight into why the Fano metric has proved to be the best practical choice in sequential decoding.
Abstract: It is shown that the metric proposed originally by Fano for sequential decoding is precisely the required statistic for minimum-error-probability decoding of variable-length codes. The analysis shows further that the "natural" choice of bias in the metric is the code rate and gives insight into why the Fano metric has proved to be the best practical choice in sequential decoding. The recently devised Jelinek-Zigangirov "stack algorithm" is shown to be a natural consequence of this interpretation of the Fano metric. Finally, it is shown that the elimination of the bias in the "truncated" portion of the code tree gives a slight reduction in average computation at the sacrifice of increased error probability.
134 citations
TL;DR: The channel is modeled with nonfrequency selective Rice and Rayleigh fading, and FEC coding with Viterbi decoding of convolutional codes, and Berlekamp-Massey decoding of Reed-Solomon codes improve the performance of the decoder.
Abstract: Fading in mobile satellite communications severely degrades the performance of data transmission. The channel is modeled with nonfrequency selective Rice and Rayleigh fading. Also, stored channel simulation is used for hardware data transmission. FEC coding with Viterbi decoding of convolutional codes, and Berlekamp-Massey decoding of Reed-Solomon codes, are used to compensate for the fading. In addition to interleaving, channel state and erasure information improve the performance of the decoder. The BER after decoding is calculated for specific codes on several channels and for different transmission schemes. Using very simple channel state and erasure information gives 2-7 dB additional coding gain. These gains have been verified by hardware data transmission on synthetic fading channels and stored mobile satellite channels.
133 citations
14 Mar 2005
TL;DR: In this paper, the decoding of Gabidulin codes is seen as an instance of reconstruction of linearized polynomials, and two efficient decoding algorithms inspired from the Welch-Berlekamp decoding algorithm for Reed-Solomon codes are presented.
Abstract: In this paper, we present a new approach of the decoding of Gabidulin codes. We show that, in the same way as decoding Reed-Solomon codes is an instance of the problem called polynomial reconstruction, the decoding of Gabidulin codes can be seen as an instance of the problem of reconstruction of linearized polynomials. This approach leads to the design of two efficient decoding algorithms inspired from the Welch–Berlekamp decoding algorithm for Reed–Solomon codes. The first algorithm has the same complexity as the existing ones, that is cubic in the number of errors, whereas the second has quadratic complexity in 2.5n2 – 1.5k2.
133 citations
TL;DR: The least storage and node computation required by a breadth-first tree or trellis decoder that corrects t errors over the binary symmetric channels is calculated.
Abstract: The least storage and node computation required by a breadth-first tree or trellis decoder that corrects t errors over the binary symmetric channels is calculated. Breadth-first decoders work with code paths of the same length, without backtracking. The Viterbi algorithm is an exhaustive trellis decoder of this type; other schemes look at a subset of the tree or trellis paths. For random tree codes, theorems about the asymptotic number of paths required and their depth are proved. For concrete convolutional codes, the worst case storage for t error sequences is measured. In both cases the optimal decoder storage has the same simple dependence on t. The M algorithm and algorithms proposed by G.J. Foschini (ibid., vol.IT-23, p.605-9, Sept. 1977) and by S.J. Simmons (PhD. diss., Queens Univ., Kingston, Ont., Canada) are optimal, or nearly so; they are all far more efficient than the Viterbi algorithm. >
133 citations
01 Aug 2014
TL;DR: Empirically the performance of polar codes at finite block lengths is boosted by moving along the family C-inter even under low-complexity decoding schemes such as, for instance, belief propagation or successive cancellation list decoder.
Abstract: We explore the relationship between polar and RM codes and we describe a coding scheme which improves upon the performance of the standard polar code at practical block lengths. Our starting point is the experimental observation that RM codes have a smaller error probability than polar codes under MAP decoding. This motivates us to introduce a family of codes that "interpolates" between RM and polar codes, call this family C-inter = {C-alpha:alpha is an element of[0;1]}, where C alpha vertical bar(alpha=1) is the original polar code, and C alpha vertical bar(alpha=0) is an RM code. Based on numerical observations, we remark that the error probability under MAP decoding is an increasing function of alpha. MAP decoding has in general exponential complexity, but empirically the performance of polar codes at finite block lengths is boosted by moving along the family C-inter even under low-complexity decoding schemes such as, for instance, belief propagation or successive cancellation list decoder. We demonstrate the performance gain via numerical simulations for transmission over the erasure channel as well as the Gaussian channel.
133 citations