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International Symposium on Wireless Communication Systems

Performance Evaluation of A Modified Sum-Product Decoding Algorithm for LDPC Codes

Stylianos Papaharalabos, P. Sweeney, B.G. Evans, G. Albertazzi, Alessandro Vanelli‐Coralli, Giovanni Emanuele Corazza

Published Dec 10, 2005• 11 citations
Publisher

Abstract

We propose a modified hyperbolic tangent (tanh) function that is used in the sum-product algorithm (SPA). This is done in order to approximate the infinite argument of the tanh function, when decoding low-density parity-check (LDPC) codes. As shown by computer simulation results, the proposed modification has a significant impact on the error floor reduction of the code and to the coding gain improvement with respect to the SPA with no modification. Computer simulation results with approximations using both piecewise linear function and coarse quantization are also presented

DOI
10.1109/iswcs.2005.1547819

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We propose a modified hyperbolic tangent (tanh) function that is used in the sum-product algorithm (SPA). This is done in order to approximate the infinite argument of the tanh function, when decoding low-density parity-check (LDPC) codes. As shown by computer simulation results, the proposed modification has a significant impact on the error floor reduction of the code and to the coding gain improvement with respect to the SPA with no modification. Computer simulation results with approximations using both piecewise linear function and coarse quantization are also presented
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.
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 paper proposes a new sum-product algorithm to improve BER performance for low-density parity-check codes. The proposed algorithm can replace multiplications and divisions with additions and subtractions by adding the logarithmic and exponential functions. In addition, the proposed algorithm can simplify both the ln[tanh(x)] and tanh-1[exp(x)] functions by using two quantization tables which can reduce tremendous computational complexity. Moreover, the simulation results show that the proposed SP algorithm can improve maximum of 0.8 dB BER performance compared with the existing modified sumproduct algorithm.
The Sum Product Algorithm (SPA) is known to offer the best performance in decoding large block length Low Density Parity Check (LDPC) codes. However, modifications in SPA to decrease the computation complexity have resulted in performance degradation. The Min Sum Algorithm (MSA) is one such variant, where the computation of the check-to-variable message is simplified to a minimum operation, instead of a hyperbolic tan calculation. Several modifications have been proposed in order to recover the performance loss of the MSA with respect to SPA. This paper proposes a modification to the MSA, based on the Wiener and Linear Minimum Mean Square Error (LMMSE) estimators for LDPC codes. The golden section search algorithm has been used to optimize the computations of the parameter estimation. Simulation results with these estimated parameters show that for low values of SNR, the modified algorithm outperforms MSA and provides performance close to that of SPA with a gain of 0.1 dB. For higher values of SNR, it outperforms MSA with a gain of 1.75 dB while providing an acceptable performance degradation with respect to SPA.
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 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.