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Digital Signal Processing

Improve Sum-Product Algorithm and Genetics-Aided for LDPC Codes

Mohammad Akbari, G. Zare Fatin, Reza Asvadi

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

In this letter, we analyze the performance of two improved Sum-Product (SP) based decoding algorithms for LDPC codes. In order to improve the decoding operation and fast convergence decoder At First, Using Averaging and using bits in the wrong equations for improve the bit node update And then by using a genetic algorithm. We corrected value bits decoding mistake is detected and value soft decision is less than 2. The decoding performance of GA-SP algorithm is superior to original SP algorithms by about 2 dB and is very close to the performance of ML decoding for (2640, 1320) Tanner LDPC code.

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In this letter, we analyze the performance of two improved Sum-Product (SP) based decoding algorithms for LDPC codes. In order to improve the decoding operation and fast convergence decoder At First, Using Averaging and using bits in the wrong equations for improve the bit node update And then by using a genetic algorithm. We corrected value bits decoding mistake is detected and value soft decision is less than 2. The decoding performance of GA-SP algorithm is superior to original SP algorithms by about 2 dB and is very close to the performance of ML decoding for (2640, 1320) Tanner LDPC code.
In order to improve the decoding performance of low density parity check (LDPC) codes, a sum-product genetic decoding (SPGD) algorithm based on genetic algorithm (GA) is proposed. By means of the classical decoding algorithm of sum-product algorithm (SPA) of LDPC codes, variable node information generated by each hard decision of iteration is regarded as individuals that constitute initial population of GA. The decoded optimal solutions are produced by a series of genetic operations. Simulation results show that under the premise of almost no increase in complexity, the proposed SPGD algorithm has the superior decoding error correction performance, better practicability and higher net coding gain (NCG).
An improvement of the forced-convergence decoding algorithm is discussed. Iterative decoding schemes such as the sum-product (SP) decoding bring out excellent performance of low-density parity check (LDPC) codes. The forced-convergence (FC) decoding is also an iterative decoding algorithm obtained by modifying the SP decoding. The FC decoding succeeds to reduce the decoding complexity of the SP decoding, but the error correcting performance is severely degraded by the modification. The performance degradation of the FC decoding is expected to be mitigated if the convergence criterion used in the algorithm is appropriately modified. This paper discusses several types of modifications of the convergence criteria. Computer simulation shows that the proposed modifications improve the performance of the FC decoding algorithm.
This letter investigates the combination of the Chase-2 and sum-product (SP) algorithms for low-density parity-check (LDPC) codes. A simple modification of the tanh rule for check node update is given, which incorporates test error patterns (TEPs) used in the Chase algorithm into SP decoding of LDPC codes. Moreover, a simple yet effective approach is proposed to construct TEPs for dealing with decoding failures with low-weight syndromes. Simulation results show that the proposed algorithm is effective in improving both the waterfall and error floor performance of LDPC codes.
In this paper, a modified sum-product algorithm to correct bit errors captured within the trapping sets, which are produced in decoding of low-density parity-check (LDPC) codes, is proposed. Unlike the original sum-product algorithm, the proposed decoding method consists of two stages. Whether the main cause of decoding failure is the trapping sets or not is determined at the first stage. And the bit errors within the trapping sets are corrected at the second stage. In the modified algorithm, the set of failed check nodes and the transition patterns of hard-decision bits are exploited to search variable nodes in the trapping sets. After inverting information of the variable nodes, the sum-product algorithm is carried out to correct the bit errors. As a result of simulation, the proposed algorithm shows continuously improved error performance with increase in the signal-to-noise ratio. It is, therefore, considered that the modified sum-product algorithm significantly reduces or possibly eliminates the error floor in LDPC codes.
Low-density parity-check (LDPC) codes are widely used in communication systems. When user messages are encoded by binary LDPC codes and transmitted with higher-order modulations, bits composing the same modulated symbol are generally correlated. Traditional soft-decision decoding algorithms for binary LDPC codes like sum-product algorithm (SPA) and min-sum algorithm (MSA) update messages only based on log-likelihood ratio (LLR) of bits, and correlations introduced by modulation are not utilized. In this paper, symbol-based SPA and MSA (S-SPA and S-MSA) which incorporate symbol-level information in the decoding procedures are proposed to provide an alternative low-cost way to better utilize available information. By narrowing the search space of symbols based on bit-level information, the complexities of the proposed algorithms are independent of modulation order. S-SPA and S-MSA achieve better error-correction performances than SPA and MSA with little additional complexities and S-MSA is friendly to hardware design of LDPC decoder.
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.