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Min-Sum Algorithm with Maximum Average Mutual Information Quantization

Zhengkang Chen, Huisheng Zhang, Lixin Li, Nan Qi

Published Jan 29, 2014• 0 citations
OpenAlex

Abstract

The specific methods of the maximum average mutual information quantization are analyzed and deduced. With this method to quantify the initial message, the variable messages and check messages are converted into integers. Then the min-sum decoding algorithm based on integer arithmetic is implemented. Simulation results demonstrate that the decoding performance of min-sum algorithm based on integer with 7-bit maximum average mutual information quantization is almost the same as that of min-sum algorithm based on integer with 8-bit uniform quantization. Meanwhile, all the variables in the algorithm are fixed-length integers, so it is convenient for hardware implementation. Although the decoding performance is slightly worse than that of the sum-product decoding algorithm, the decoding time is greatly reduced. So it is very convenient for future generation communication.

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The specific methods of the maximum average mutual information quantization are analyzed and deduced. With this method to quantify the initial message, the variable messages and check messages are converted into integers. Then the min-sum decoding algorithm based on integer arithmetic is implemented. Simulation results demonstrate that the decoding performance of min-sum algorithm based on integer with 7-bit maximum average mutual information quantization is almost the same as that of min-sum algorithm based on integer with 8-bit uniform quantization. Meanwhile, all the variables in the algorithm are fixed-length integers, so it is convenient for hardware implementation. Although the decoding performance is slightly worse than that of the sum-product decoding algorithm, the decoding time is greatly reduced. So it is very convenient for future generation communication.
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) codes enjoy the good properties of approaching the Shannon limit, and its practical application is of great significance. In this paper, the decoding algorithm of LDPC codes for eight-phase-shift keying modulation is particularly studied, and the specific methods of the maximum average mutual information quantisation are analysed and deduced. With this method to quantify the initial message, the variable messages and check messages are converted into integers when each iteration has been finished, and then the min-sum decoding algorithm based on integer arithmetic is implemented. Simulation results demonstrate that the performance of the min-sum decoding algorithm with maximum average mutual information quantisation is close to that of the high-precision floating-point sum-product decoding algorithm. Meanwhile, It is convenient for hardware implementation since all the variables in the algorithm are fixed-length integers. Although the bit error rate is slightly worse than that of the sum-product decoding algorithm, the decoding time consumption is greatly reduced.
Low density parity check (LDPC) codes enjoy the good properties of approaching the Shannon limit, and its practical application is of great significance. In this paper, the decoding algorithm of LDPC codes for eight-phase-shift keying modulation is particularly studied, and the specific methods of the maximum average mutual information quantisation are analysed and deduced. With this method to quantify the initial message, the variable messages and check messages are converted into integers when each iteration has been finished, and then the min-sum decoding algorithm based on integer arithmetic is implemented. Simulation results demonstrate that the performance of the min-sum decoding algorithm with maximum average mutual information quantisation is close to that of the high-precision floating-point sum-product decoding algorithm. Meanwhile, It is convenient for hardware implementation since all the variables in the algorithm are fixed-length integers. Although the bit error rate is slightly worse than that of the sum-product decoding algorithm, the decoding time consumption is greatly reduced.
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.
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.