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On soft-decision iterative decoding algorithms by using algebraic decoding for RS codes

Hitoshi Tokushige, I. Hisadomi, Tadao Kasami

Published Mar 22, 2004• 3 citations
Publisher

Abstract

We consider an iterative decoding algorithm by using algebraic decoding for non-binary codes. In the decoding algorithm, algebraic decoding are carried out with respect to successively chosen input words, called the search centers. We present a new method for selecting sequences of search centers of algebraic decoding. Over the AWGN channel using BPSK signaling, we show simulation results on the error performances of the iterative decoding algorithms whose search centers are given by the proposed method, abbreviated IAD, for Reed-Solomon codes. From the simulation results, IAD provides considerably better error performance than GMD and CGA decoding with the same number of iterations.

DOI
10.1109/glocom.2002.1188353

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We consider an iterative decoding algorithm by using algebraic decoding for non-binary codes. In the decoding algorithm, algebraic decoding are carried out with respect to successively chosen input words, called the search centers. We present a new method for selecting sequences of search centers of algebraic decoding. Over the AWGN channel using BPSK signaling, we show simulation results on the error performances of the iterative decoding algorithms whose search centers are given by the proposed method, abbreviated IAD, for Reed-Solomon codes. From the simulation results, IAD provides considerably better error performance than GMD and CGA decoding with the same number of iterations.
This letter considers an iterative decoding algorithm for non-binary linear block codes in which erasure and error decoding is performed for input words given by the sums of a hard-decision received sequence and given test patterns. We have proposed a new selection method of test patterns for the iterative decoding algorithm. Simulation results have shown that the decoding algorithm with test patterns by the proposed selection method provides better error performance than a conventional iterative decoding algorithm with the same number of the error and erasure decoding iterations over an additive white Gaussian noise channel using binary phase-shift keying modulation.
In this letter, a deep learning based iterative soft decision decoding algorithm for Reed-Solomon codes is proposed. This algorithm takes advantage of deep neural network and Stochastic Shifting based Iterative Decoding (SSID). By assigning weights to every edge in the Tanner graph and changing the architecture of SSID method, the proposed neural network decoder achieves better decoding performance. Compared with BM decoding, HDD-LCC and traditional SSID, simulation results show that for RS (15, 11), this algorithm provides coding gain up to 1.5dB, 1.1dB and 0.5dB, respectively when FER = 10-2.
SUMMARY In this paper, we consider sufficient conditions for ruling out some useless iteration steps in a class of softdecision iterative decoding algorithms for binary block codes used over the AWGN channel using BPSK signaling. Sufficient conditions for ruling out the next single decoding step, called ruling-out conditions and those for ruling out all the subsequent iteration steps, called early termination conditions, are formulated in a unified way without degradation of error performance. These conditions are shown to be a type of integer programming problems. Several techniques for reducing such an integer programming problem to a set of subprograms with smaller computational complexities are presented. As an example, an early termination condition for Chase-type decoding algorithm is presented. Simulation results for the (64, 42, 8) Reed-Muller code and (64, 45, 8) extended BCH code show that the early termination condition combined with a ruling-out condition proposed previously is considerably effective in reducing the number of test error patterns, especially as the total number of test error patterns concerned grows.
Bit-by-bit soft-decision decoding of binary cyclic codes is considered. A significant reduction in decoder complexity can be achieved by requiring only that the decoder correct all analog error patterns which fall within a Euclidean sphere whose radius is equal to half the minimum Euclidean distance of the code. Such a "maximum-radius" scheme is asymptotically optimum for the additive white Gaussian noise (AWGN) channel. An iterative extension of the basic algebraic analog decoding scheme is discussed, and performance curves are given for the (17,9), (21,11), and (73,45) codes on the AWGN channel.