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International Conference on Ubiquitous Information Management and Communication (IMCOM)

Simplified sum-product algorithm using piecewise linear function approximation for low complexity LDPC decoding

Jae Hee Han, Myung Hoon Sunwoo

Published Feb 15, 2009• 7 citations
Publisher

Abstract

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.

DOI
10.1145/1516241.1516294

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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 new simplified sum-product (SSP) decoding algorithm to improve BER performance for low-density parity-check codes. The proposed SSP algorithm can replace multiplications and divisions with additions and subtractions without extra computations. In addition, the proposed SSP algorithm can simplify both the ln[tanh(x)] and exp[tanh-1(x)] by using two quantization tables which can reduce tremendous computational complexity. Moreover, the simulation results show that the proposed SSP algorithm can improve about 0.3~0.8 dB of BER performance compared with the existing modified sum-product algorithm.
This paper proposes new simplified sum-product (SSP) decoding algorithm to improve BER performance for low-density parity-check codes. The proposed SSP algorithm can replace multiplications and divisions with additions and subtractions without extra computations. In addition, the proposed SSP algorithm can simplify both the In[tanh(x)] and tanh-1 [exp(x)] by using two quantization tables which can reduce tremendous computational complexity. Moreover, the simulation results show that the proposed SSP algorithm can improve about of BER performance compared with the existing modified sum-product algorithms.
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 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.
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
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.