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IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)

Very-low-complexity decoding algorithm for low-density parity-check codes

Hui-Shi Song, Ping Zhang

Published Jul 8, 2004• 2 citations
Publisher

Abstract

In this paper, we propose a new very-low-complexity (VLC) decoding algorithm for low-density parity-check (LDPC) codes. This new algorithm only need subtract a correcting factor to improve the accuracy of the soft message values delivered by a previously proposed simplified belief-propagation (BP)-based algorithm called uniformly most powerful (UMP) algorithm. However, the VLC algorithm outperforms the UMP algorithm greatly. The correcting factor can be obtained by simulation or theoretical derivation. This new VLC algorithm is much simpler to implement than BP algorithm, and also simpler than previously proposed normalized BP-based algorithm in which the operation of dividing a normalization factor is needed. However, the performance of the VLC algorithm is slightly better than that of the normalized BP-based algorithm. Also, the VLC algorithm is universal in that the decoding is independent of the channel characteristics. Simulation results demonstrate that the performance of the new VLC algorithm can nearly approach that of BP on the additive white Gaussian noise (AWGN) channel.

DOI
10.1109/pimrc.2003.1264253

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In this paper, we propose a new very-low-complexity (VLC) decoding algorithm for low-density parity-check (LDPC) codes. This new algorithm only need subtract a correcting factor to improve the accuracy of the soft message values delivered by a previously proposed simplified belief-propagation (BP)-based algorithm called uniformly most powerful (UMP) algorithm. However, the VLC algorithm outperforms the UMP algorithm greatly. The correcting factor can be obtained by simulation or theoretical derivation. This new VLC algorithm is much simpler to implement than BP algorithm, and also simpler than previously proposed normalized BP-based algorithm in which the operation of dividing a normalization factor is needed. However, the performance of the VLC algorithm is slightly better than that of the normalized BP-based algorithm. Also, the VLC algorithm is universal in that the decoding is independent of the channel characteristics. Simulation results demonstrate that the performance of the new VLC algorithm can nearly approach that of BP on the additive white Gaussian noise (AWGN) channel.
In this paper, we propose a belief-propagation (BP)-based decoding algorithm which utilizes normalization to improve the accuracy of the soft values delivered by a previously proposed simplified BP-based algorithm. The normalization factors can be obtained not only by simulation, but also, importantly, theoretically. This new BP-based algorithm is much simpler to implement than BP decoding as it requires only additions of the normalized received values and is universal, i.e., the decoding is independent of the channel characteristics. Some simulation results are given, which show this new decoding approach can achieve an error performance very close to that of BP on the additive white Gaussian noise channel, especially for low-density parity check (LDPC) codes whose check sums have large weights. The principle of normalization can also be used to improve the performance of the max-log-MAP algorithm in turbo decoding, and some coding gain can be achieved if the code length is long enough.
In this paper, we propose a new reduced-complexity decoding algorithm of Low-Density Parity-Check (LDPC) codes, called Belief-Propagation-Approximated (BPA) algorithm, which utilizes the idea of normalization and translates approximately the intricate nonlinear operation in the check nodes of the original BP algorithm to only one operation of looking up the table. The normalization factors can be obtained by simulation, or theoretically. Simulation results demonstrate that BPA algorithm exhibits fairly satisfactory bit error performance on the Additive White Gaussian Noise (AWGN) channel.
In this paper, we propose a new reduced-complexity decoding algorithm of Low-Density Parity-Check (LDPC) codes, called Belief-Propagation-Approximated (BPA) algorithm, which utilizes the idea of normaliza-tion and translates approximately the intricate nonlinear operation in the check nodes of the original BP algorithm to only one operation of looking up the table. The normalization factors can be obtained by simulation, or theoretically. Simulation results demonstrate that BPA algorithm exhibits fairly satisfactory bit error performance on the Additive White Gaussian Noise (AWGN) channel.
A uniformly most powerful (UMP) belief propagation (BP) based algorithm is referred to as a simplified version of a BP algorithm with reduced complexity but performance loss for low density parity check (LDPC) codes. To compensate the performance loss, the normalized BP based algorithm was proposed, where the normalization factor was derived by mean ratio or by minimizing the mean square error. In this paper, an improved novel normalized BP based algorithm is proposed. The normalization uses multiplicative factor instead of divisional factor. The novel scheme shows better performance than the existing normalized BP based algorithms while keeping the same implementation complexity. The simulation is done for two kinds of LDPC codes: random constructed codes and finite geometry codes. At high signal-to-noise ratio (SNR) region, the proposed scheme can achieve even better performance than BP algorithm for short length random constructed LDPC codes.
In this paper, we propose the modified uniformly most powerful (UMP) belief-propagation (BP)-based decoding algorithm which utilizes multiplicative and additive factors to diminish the errors introduced by the approximation of the soft values given by a previously proposed UMP BP-based algorithm. This modified UMP BP-based algorithm shows better performance than that of the normalized UMP BP-based algorithm, i.e., it has an error performance closer to BP than that of the normalized UMP BP-based algorithm on the additive white Gaussian noise channel for low density parity check codes. Also, this algorithm has the same complexity in its implementation as the normalized UMP BP-based algorithm.
An improved decoding algorithm based on minimum mean square error(MMSE) for low-density parity-check(LDPC) codes is proposed.The new algorithm combines processing methods of two modified uniformly most powerful(UMP) BP-based algorithms(normalized UMP BP-based algorithm and offset UMP BP-based algorithm) and attains the corresponding normalization factor and offset factor according to MMSE criterion.Simulations indicate that,compared with the two above-mentioned algorithms,a gain of 0.03 dB can be achieved at bit error rate(BER) of 10-6 with the proposed algorithm when a(3,6) regular LDPC code of code length 1 008 and code rate 1/2 is used.