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Min-sum Integer Decoding for LDPC in QPSK Modulation

Peng Xin

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

Low-Density Parity-Check(LDPC) codes are typical of preeminent performance approaching Shannon’s capacity limit.This paper studies the LDPC codes min-sum decoding algorithm,and a min-sum algorithm in QPSK modulation based on integer operation is proposed for decoding LDPC codes.All the variables are fixed length integers in this algorithm,so it is very convenient for hardware implementation.Simulation results show that its performance is close to that of sum-product algorithm whose variables are high precision floating point numbers.

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Low-Density Parity-Check(LDPC) codes are typical of preeminent performance approaching Shannon’s capacity limit.This paper studies the LDPC codes min-sum decoding algorithm,and a min-sum algorithm in QPSK modulation based on integer operation is proposed for decoding LDPC codes.All the variables are fixed length integers in this algorithm,so it is very convenient for hardware implementation.Simulation results show that its performance is close to that of sum-product algorithm whose variables are high precision floating point numbers.
The LDPC codes decoding algorithm over additive white gaussian noise(AWGN) channels was studied,and a min-sum algorithm based on integer operation was proposed for decoding LDPC codes.All the variables were fixed length integers in this algorithm,which was very convenient for hardware implementation.At the signal-to-noise ratios(SNR) above 3dB,its performance was equal to that of sum-product algorithm whose variables were high precision floating point numbers.Also,a coefficient was designed to modify the min-sum algorithm,whose decoding performance was improved greatly especially at low SNR.And another achievement had been found that this algorithm had a lower error floor at high SNR.
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.
Abstract ― Low Density Parity Check (LDPC) code approaches Shannon–limit performance for binary field and long code lengths. However, performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program, and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that the proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.
Low Density Parity Check (LDPC) code approaches Shannon–limit performance for binary field and long code lengths. However, performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program, and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that the proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.
The decoding algorithm of low-density parity-check(LDPC) codes in quaternary phase shift keying(QPSK) modulation is in-depth studied.The specific method of the maximum average mutual information quantization is analyzed and deduced.With this method to quantify the initial message,each iteration of the variable messages and check messages becomes integer,then the min-sum decoding algorithm based on integer arithmetic is implemented.Simulation results show that the performance of the min-sum decoding algorithm with maximum average mutual information quantization is about 0.39 dB worse than the performance of high-precision floating-point sum-product decoding algorithm.At the same time all the variables in the algorithm are fixed-length integers,so it is easy to implement in hardware.Although the decoding performance is slightly worse than sum-product decoding performance,the decoding time is greatly reduced.
Low Density Parity Check (LDPC) approaches Shannon -limit performance for binary field and long code lengths. However performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that the proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding, while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.