Near optimum universal belief propagation based decoding of low-density parity check codes

TLDR

The paper proposes a belief‑propagation decoding algorithm that uses normalization to improve the accuracy of soft values produced by a simplified BP scheme. The algorithm derives normalization factors analytically or via simulation, performs only additions of normalized received values, is simpler than conventional BP, universal across channel types, and its normalization principle can also enhance max‑log‑MAP turbo decoding for sufficiently long codes. Simulations show the decoder achieves error performance very close to BP on the AWGN channel, especially for LDPC codes with large check sums, and that the normalization principle yields coding gains for long turbo codes.

Abstract

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.