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A Novel Modified Algorithm with Reduced Complexity LDPC Code Decoder

Yang Song, Nanhai Bao, Cai Chaoshi

Published Oct 1, 2014• 0 citations
OpenAlex

Abstract

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.

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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.
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.
The authors deal with the sum–product algorithm (SPA) based on the hyperbolic tangent (tanh) rule when it is applied for decoding low-density parity-check (LDPC) codes. Motivated by the finding that, because of the large number of multiplications required by the algorithm, an overflow in the decoder may occur, two novel modifications of the tanh function (and its inverse) are proposed. By means of computer simulations, both methods are evaluated using random-based LDPC codes with binary phase shift keying (BPSK) signals transmitted over the additive white Gaussian noise (AWGN) channel. It is shown that the proposed modifications improve the bit error rate (BER) performance up to 1 dB with respect to the conventional SPA. These results have also shown that the error floor is removed at BER lower than 10−6. Furthermore, two novel approximations are presented to reduce the computational complexity of the tanh function (and its inverse), based on either a piecewise linear function or a quantisation table. It is shown that the proposed approximations can slightly improve the BER performance (up to 0.13 dB) in the former case, whereas small BER performance degradation is observed (<0.25 dB) in the latter case. In both cases, however, the decoding complexity is reduced significantly.
Among the decoding algorithms for low-density parity-check(LDPC) code,sum-product algorithm(SPA) has the optimal performance but high complexity,while min-sum algorithm has simple implementation complexity but worse performance.Considering this performance-complexity contradiction,some modified min-sum algorithms are proposed.In this paper,researches are done based on one of the modified min-sum algorithms that is close to SPA in performance but the way modifying fraction works is simplified.Simplified algorithm remains similar in performance to sum-product algorithm but has a remarkably reduced implementation complexity.
This paper proposes the simplified sum-product (SSP) decoding algorithm to improve BER performance for low-density parity-check codes (LDPC). The sum-product algorithm achieves the highest BER performance among the LDPC decoding algorithms. However, based on the hyperbolic tangent and inverse hyperbolic tangent functions for the check node updates, the sum-product (SP) algorithm requires high computational complexity. To reduce computational complexity, the proposed SSP algorithm adopts a piecewise linear approximation, the logarithmic and exponential functions, which can replace multiplications and divisions with additions and subtractions. In addition, the proposed SSP algorithm can simplify both the ln[tanh(x)] and tanh-1[exp(x)] by using two quantization tables which can reduce tremendous computational complexity. Simulation results show that the proposed SSP algorithm can improve about 0.8 dB of bit error ratio (BER) performance compared with the modified sum-product algorithm.
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.
An improved decoding algorithm for low-density parity-check (LDPC) codes is presented. By taking advantages of the first-term Taylor’s series multiple 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. Besides, the parameter δ is introduced to determine suitable expansion points. The simulation result shows that the proposed method with ten expansion points when δ is set to 0.01 has almost identical performance compared with ideal SPA algorithm and outperforms both the min-sum algorithm (MS), the offset min-sum algorithm (OMS) and the normalised min-sum algorithm (NMS). The architecture of proposed method is also presented for implementation, which has reduced computational complexity and is feasible for hardware implementation.