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IEEE International Symposium on Information Theory (ISIT)

Near optimum universal belief propagation based decoding of LDPC codes and extension to turbo decoding

J. Chen, M.P.C. Fossorier

Published Nov 13, 2002• 12 citations
Publisher

Abstract

In this paper, we propose a normalized belief propagation-based algorithm which utilizes normalization to improve the accuracy of the soft values delivered by a previously proposed simplified belief propagation-based algorithm, and can achieve an error performance very close to that of belief propagation. We also extend the principle of normalization to improve the performance of the Max-Log-MAP algorithm in turbo decoding.

DOI
10.1109/isit.2001.936052

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•Jul 17, 2012•1 citation
In this paper, we propose a normalized belief propagation-based algorithm which utilizes normalization to improve the accuracy of the soft values delivered by a previously proposed simplified belief propagation-based algorithm, and can achieve an error performance very close to that of belief propagation. We also extend the principle of normalization to improve the performance of the Max-Log-MAP algorithm in turbo decoding.
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.
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 letter, we analyze the performance of two improved belief propagation (BP) based decoding algorithms for LDPC codes, namely the normalized BP-based and the offset BP-based algorithms, by means of density evolution. The numerical calculations show that with one properly chosen parameter for each of these two improved BP-based algorithms, performances very close to that of the BP algorithm can be achieved. Simulation results for LDPC codes with code length moderately long validate the proposed optimization.