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Asilomar Conference on Signals, Systems and Computers (ACSSC)

Hard Decision Error Correcting Scheme Based on LDPC Codes over Impulse Noise Channels

Miloš Ivković, Shuguang Robert Cui

Published Jan 1, 2006• 0 citations
Publisher

Abstract

We investigate hard decision based low-density parity-check (LDPC) codes over an impulse noise channel, which is modeled as the concatenation of a Binary Erasure Channel (BEC) and a Binary Symmetric Channel (BSC). We propose a decoding algorithm based on three-state quantization of the traditional sum-product algorithm, where the three states correspond to "1", "0", and "E" (Erasure). As such, the proposed algorithm dramatically reduces the implementation complexity, while still keeps satisfactory decoding performance as shown by simulation results.

DOI
10.1109/acssc.2006.355160

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We investigate hard decision based low-density parity-check (LDPC) codes over an impulse noise channel, which is modeled as the concatenation of a Binary Erasure Channel (BEC) and a Binary Symmetric Channel (BSC). We propose a decoding algorithm based on three-state quantization of the traditional sum-product algorithm, where the three states correspond to "1", "0", and "E" (Erasure). As such, the proposed algorithm dramatically reduces the implementation complexity, while still keeps satisfactory decoding performance as shown by simulation results.
This paper investigates decoding of low-density parity-check (LDPC) codes over the binary erasure channel (BEC). We study the iterative and maximum-likelihood (ML) decoding of LDPC codes on this channel. We derive bounds on the ML decoding of LDPC codes on the BEC. We then present an improved decoding algorithm. The proposed algorithm has almost the same complexity as the standard iterative decoding. However, it has better performance. Simulations show that we can decrease the error rate by several orders of magnitude using the proposed algorithm. We also provide some graph-theoretic properties of different decoding algorithms of LDPC codes over the BEC which we think are useful to better understand the LDPC decoding methods, in particular, for finite-length codes.
An improved decoding algorithm for low-density parity-check code(LDPC) on finite-state Markov channels was presented and the corresponding factor graph representation was given.It consists of two parts: standard sum-product algorithm(SPA) for LDPC and forward-backward(FB) algorithm for Markov channel.After each iteration for SPA,FB re-estimated the channel likelihood ratio for the next iteration of SPA based on soft decisions for noise bits from SPA.Considering more cycles in the factor graph with the introduction of the Markov channel node,the probabilistic schedule was used to update the message during the iterations for decoding.Simulation results show that the algorithm not only performs much better than the standard sum-product algorithm,but also outperforms the algorithm based on hard decisions for noise bits.
A method for estimating the performance of low-density parity-check (LDPC) codes decoded by hard-decision iterative decoding algorithms on binary symmetric channels (BSC) is proposed. Based on the enumeration of the smallest weight error patterns that cannot be all corrected by the decoder, this method estimates both the frame error rate (FER) and the bit error rate (BER) of a given LDPC code with very good precision for all crossover probabilities of practical interest. Through a number of examples, we show that the proposed method can be effectively applied to both regular and irregular LDPC codes and to a variety of hard-decision iterative decoding algorithms. Compared with the conventional Monte Carlo simulation, the proposed method has a much smaller computational complexity, particularly for lower error rates.
Low Density Parity Check (LDPC) codes are one of the block coding techniques that can approach the Shannon’s limit within a fraction of a decibel for high block lengths. In many digital communication systems, these codes have strong competitors of turbo codes for error control. LDPC codes performance depends on the excellent design of parity check matrix and many diverse research methods have been used by different study groups to evaluate the performance. Unlike many other classes of codes, LDPC codes are already equipped with a fast, probabilistic decoding algorithm. This makes LDPC codes not only attractive from a theoretical point of view, but also very suitable for practical applications. This paper throws hard decision and soft decision algorithm of LDPC. The hard decision algorithm contains Bit flipping algorithm and Soft decoding algorithm contains Sum product algorithm which is used to correct burst error. Sum Product algorithm is also called as belief propagation. Bit flipping and Sum Product algorithms are explained and can be implemented for the generated parity check matrix of (1016x508) for LDPC code with code rate 1/2.