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Electronics Letters

Fast decoding of LDPC codes using quantisation

Yucheng He, Shaohui Sun, Xinmei Wang

Published Feb 14, 2002• 8 citations
Publisher

Abstract

A very fast quantised belief propagation algorithm is proposed for decoding low-density parity-check codes. This algorithm enables flexible quantisation schemes with low complexity and good performance near to or even better than that of continuous decoding. It can lower the error floor at high signal-to-noise ratios.
DOI
10.1049/el:20020131

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A fast quantized belief propagation algorithm is proposed for decoding low-density parity-check(LDPC) codes. With operations performed by addressing tables, the proposed algorithm takes as operands the indices of labels rather than the quantization levels. The intermediate calculations have been contained in operation tables with much higher precision. The required storage can be significantly reduced by applying the symmetry property while keeping low time complexity. Without the increase in time complexity, it is convenient to realize the decoding with uniform quantization or any nonuniform quantizations that is designed for improving the performance. The time-varying decoder also becomes possible. This algorithm makes it possible to apply LDPC codes to practical systems or to realize fast simulation systems. Some simulation results are also given. The 6?bit logarithmic quantization results in gains of about 0.2?dB relative to the uniform one, approaching to the continuous decoding at low signal-to-noise ratios (SNRs) and yielding a loss of about 0.2?dB at high SNRs. Proper quantization of high order can achieve the performance of continuous decoding, and it may be superior to continuous decoding at high SNRs.
A hybrid belief propagation (BP) decoding algorithm for low-density parity-check code is proposed to accelerate the convergence of decoding and reduce the number of decoding iterations. The hybrid scheme is presented by integrating the BP algorithm with the bit-flipping function which is used as adaptive weighted factor in the BP iteration decoding. The adaptive weighting factor is based on the average weighted reliability measure of the hard output of decoder. The proposed hybrid adaptive weighted iteration scheme can efficiently increase the convergence speed of the belief propagation decoding and therefore improve the error performance. Simulation results show that the proposed algorithm can significantly reduce the decoding complexity and achieve better error performances as compared with the sum-product algorithm.
The quantization scheme for the iterative belief propagation (BP) algorithm of low density parity check (LDPC) codes is studied.The effects of the bound,resolution,and other parameters for uniform and nonuniform quantization schemes are discussed.Good performance of decoding under properly designed quantization can be obtained as shown by simulations.Furthermore,we found that the quantization of high order for the mid variables of BP decoding algorithm can improve the performance and reduce the error floor of LDPC codes at regions of high signal to noise ratio.
At the heart of modern coding theory lies the fact that low-density parity-check (LDPC) codes can be efficiently decoded by belief propagation (BP). The BP is an inference algorithm which operates on a graphical model of a code, and lends itself to low-complexity and high-speed implementations, making it the algorithm of choice in many applications. It has unprecedentedly good error rate performance, so good that when decoded by the BP, LDPC codes approach theoretical limits of channel capacity. However, this capacity approaching property holds only in the asymptotic limit of code length, while codes of practical lengths suffer abrupt performance degradation in the low noise regime known as the error floor phenomenon. Our study of error floor has led to an interesting and surprising finding that it is possible to design iterative decoders which are much simpler yet better than belief propagation! These decoders do not propagate beliefs but a rather different kind of messages that reflect the local structure of the code graph. This has opened a plethora of exciting theoretical problems and applications. This paper introduces this new paradigm.
Summary The simplicity of decoding is one of the most important characteristics of the low density parity check (LDPC) codes. Belief propagation (BP) decoding algorithm is a well‐known decoding algorithm for LDPC codes. Most LDPC codes with long lengths have short cycles in their Tanner graphs, which reduce the performance of the BP algorithm. In this paper, we present 2 methods to improve the BP decoding algorithm for LDPC codes. In these methods, the calculation of the variable nodes is controlled by using “multiplicative correction factor” and “additive correction factor.” These factors are obtained for 2 separate channels, namely additive white Gaussian noise (AWGN) and binary symmetric channel (BSC), as 2 functions of code and channel parameters. Moreover, we use the BP‐based method in the calculation of the check nodes, which reduces the required resources. Simulation results show the proposed algorithm has better performance and lower decoding error as compared to BP and similar methods like normalized‐BP and offset‐BP algorithms.