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Journal of Information and Computational Science

Taylor Series Based Decoding Algorithm for Complexity Reduction of LDPC Codes

Yang Song

Published Mar 1, 2014• 0 citations
Publisher

Abstract

A novel effective decoding algorithm for LDPC codes is proposed, which significantly simplifies the check node update computation of the Sum-Product Algorithm (SPA). Through simplified Taylor Series algorithm, It made index operation for multiplication and addition operations in the check node update. Compared with the existing approximations, the proposed method is less computational complexity than SPA algorithm, simulation results show that the proposed algorithm can achieve an error performance better than the Min-sum (MS) algorithm with small increase computational complexity.

DOI
10.12733/jics20103028

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A novel effective decoding algorithm for LDPC codes is proposed, which significantly simplifies the check node update computation of the Sum-Product Algorithm (SPA). Through simplified Taylor Series algorithm, It made index operation for multiplication and addition operations in the check node update. Compared with the existing approximations, the proposed method is less computational complexity than SPA algorithm, simulation results show that the proposed algorithm can achieve an error performance better than the Min-sum (MS) algorithm with small increase computational complexity.
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A simple,yet effective decoding algorithm for LDPC(low-density parity-check) codes over GF(q) is presented.By taking advantages of the first-term Taylor's series expansion to approximate the correction term of the Jacobian logarithm used in LLR-SPA(log-likelihood ratio sum-product algorithm),we propose an algorithm which significantly simplifies the check node update computation of the optimal LLR-SPA.Compared to the offset min-sum algorithm,the proposed algorithm achieves a gain of about 0.2dB at the BER of 10-4.Moreover,unlike the offset min-sum algorithm,parameters of this algorithm are independent of the order of the Galois Filed.
This letter proposes a new algorithm for the check node update in the decoding of low-density parity-check (LDPC) codes. The proposed algorithm is based on a new approximation formula of standard sum-product algorithm (SPA) which can reduce the approximation error of min-sum algorithm (MSA) and has almost the same performance as sum-product algorithm (SPA) under both floating precision operation and fixed-point operation. Besides, the new approximation formula can be implemented in simple structures competitive with MSA.
A novel efficient decoding algorithm reduced the sum-product algorithm (SPA) Complexity with LPDC code is proposed. Base on the hyperbolic tangent rule, modified the Check node update with two horizontal process, which have similar calculation, Motivated by the finding that sun- min (MS) algorithm reduce the complexity reducing the approximation error in the horizontal process, simplify the information weight small part. Compared with the exiting approximations, the proposed method is less computational complexity than SPA algorithm. Simulation results show that the author algorithm can achieve performance very close SPA.
This paper proposes a low-complexity LDPC decoding algorithm with simplified check nodes updating. The proposed algorithm simplifies the result of the second-minimum in check nodes based on the first-minimum computation instead of computing it directly. In order to obtain the approximate result, effective corrected coefficients are utilized, which can reduce the complexity by eliminating the complex computations. Complexity analysis is provided and the results indicate that the complexity of the proposed algorithm is much lower than the general NMS algorithm and MS-based simplified algorithms. Simulation results show that the performance of the proposed algorithm can closely match the NMS algorithm with the same number of iterations.
A simplified decoding algorithm for low-density parity-check (LDPC) codes over high order Galois field is proposed to reduce the complexity of traditional sum-product algorithm (SPA). There are only addition operation and comparison operation in this algorithm, without complex multiplication operation. The computation complexity of proposed algorithm is much smaller than the SPA. The signal-to-noise power ratio (SNR) isn't needed in this algorithm, so the process of SNR estimation can also be removed. The simulation results show that the bit error rate (BER) performance of proposed algorithm degrades only about 0.5 dB than the SPA, so the proposed algorithm is an efficient simplified algorithm in engineering.