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Automation and Remote Control

Algorithm of multithreshold decoding for Gaussian channels

V. V. Zolotarev, Gennady V. Ovechkin

Published Jun 1, 2008• 9 citations
Publisher

Abstract

Major principles of the method of the linear codes multithreshhold decoding as search for the global functional extremum for a great number of variables are considered. It was demonstrated that the multithreshold decoding efficiency is close to the results ensured by the optimum exhaustive search methods. Decoding complexity under software and hardware realizations is evaluated.

DOI
10.1134/s0005117908060180

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Major principles of the method of the linear codes multithreshhold decoding as search for the global functional extremum for a great number of variables are considered. It was demonstrated that the multithreshold decoding efficiency is close to the results ensured by the optimum exhaustive search methods. Decoding complexity under software and hardware realizations is evaluated.
Forward error correction technique based on the optimization procedures for multithreshold decoding algorithms is considered. Recent advances as well as new opportunities of the multithreshold decoders for use in the systems working at the Shannon’s limit are analysed. Performances of the multithreshold decoders for self-orthogonal binary and non-binary codes over Gaussian channels are presented. Simulation results of BER performance of proposed decoder is shown to be close to the results provided by optimum total search methods.
Multithreshold decoders (MTD) of self-orthogonal codes (SOC) for erasure channels implementing error correction methods based on searching global extremum of functions in discrete spaces are considered. To increase the efficiency of erasure recoveries the concatenated codes comprising inner SOC and outer codes being simple for decoding such as parity-check codes, Hamming codes or BCH codes are offered. The usage of the codes offered provides efficient erasure recovery when operating near channel capacity with linear decoder complexity. The questions of high-throughput software MTD implementation recovering erasures using GPU are considered. The MTD versions developed are shown to be able to perform data flow decoding with the rate of several hundred MB/s using GPU.
A new efficient method is developed for optimal maximum likelihood (ML) decoding of an arbitrary binary linear code based on data received from a Gaussian channel. The decoding algorithm is based on minimization of a difference of two monotonic objective functions subject to the 0-1 constraint of bit variables. The iterative process converges to the global optimal ML solution after a finite number of steps. The proposed algorithm's computational complexity depends on the input sequence length k which is much less than the codeword length n, especially for codes with small code rates. The viability of the developed method is verified through simulations on different coding schemes