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Communications technology

Research on Decoding Algorithm of LDPC Code

Cai Can-hui

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

Based on the demand for hardware implementation,the paper presents the decoding algorithm of LDPC code and proposes a new modification factor for Normalized Min-Sum algorithm to ease the hardware implementation.This paper describes the simulations on the performances of quantization range and quantization scheme.Simulation results show that the performances of 5,6 or 7 quantization bits are all quite close to ideal performance.This algorithm would reduce greatly the computation complexity and the difficulty in hardware implementation.

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Based on the demand for hardware implementation,the paper presents the decoding algorithm of LDPC code and proposes a new modification factor for Normalized Min-Sum algorithm to ease the hardware implementation.This paper describes the simulations on the performances of quantization range and quantization scheme.Simulation results show that the performances of 5,6 or 7 quantization bits are all quite close to ideal performance.This algorithm would reduce greatly the computation complexity and the difficulty in hardware implementation.
It's common to use high-precision floating-point operations on theoretical study of the Low Density Parity Check (LDPC) codes, but it is difficult to implement it in practical application. Therefore, there is a great need to design effective quantitative method which enables us to implement it in hardware easily. In this paper, the min-sum decoding algorithm of LDPC codes for 8PSK modulation is studied in detail, and the method of the uniform quantization is analyzed and deduced. With this method to quantify the initial message, the variable messages and check messages are converted into integers after each iteration. Then the min-sum decoding algorithm based on integer arithmetic for 8PSK modulation is implemented. Simulation results demonstrate that the performance of the min-sum decoding algorithm with the uniform quantization is close to that of the high-precision floating-point sum-product decoding algorithm. Meanwhile, all the variables in the algorithm are fixed-length integers, so it is convenient for hardware implementation.
The effects of clipping and quantization on the performance of the min-sum algorithm for the decoding of low-density parity-check (LDPC) codes at short and intermediate block lengths are studied. It is shown that in many cases, only four quantization bits suffice to obtain close to ideal performance over a wide range of signal-to-noise ratios. Moreover, we propose modifications to the min-sum algorithm that improve the performance by a few tenths of a decibel with just a small increase in decoding complexity. A quantized version of these modified algorithms is also studied. It is shown that, when optimized, modified quantized min-sum algorithms perform very close to, and in some cases even slightly outperform, the ideal belief-propagation algorithm at observed error rates.
This paper is concerned with the implementation issues of the so-called min-sum algorithm (also referred to as max-sum or max-product) for the decoding of low-density parity-check (LDPC) codes. The effects of clipping threshold and the number of quantization bits on the performance of the min-sum algorithm at short and intermediate block lengths are studied. It is shown that min-sum is robust against quantization effects, and in many cases, only four quantization bits suffices to obtain close to ideal performance. We also propose modifications to the min-sum algorithm that improve the performance by a few tenths of a dB with just a small increase in decoding complexity.
The simple algorithms based on belief propagation algorithm of LDPC codes are studied.A modified algorithm which integrates Row Message Passing schedule with Offset Min-Sum algorithm for decoding LDPC codes is proposed.The proposed algorithm facilitates hardware implementation because it improves the convergence property while its computation complexity is the same as Offset Min-Sum algorithm,and it reduces the storage for the optimized memory method.The simulation results demonstrate that the proposed algorithm reduces the average iterations and quantization implementation memory.
Decoding algorithms with strong practical value not only have good decoding performance, but also have the computation complexity as low as possible. For this purpose, the paper points out the modified min-sum decoding algorithm(M-MSA). On the condition of no increasing in the decoding complexity, it makes the error-correcting performance improved by adding the appropriate scaling factor based on the min-sum algorithm(MSA), and it is very suitable for hardware implementation. Simulation results show that this algorithm has good BER performance, low complexity and low hardware resource utilization, and it would be well applied in the future.