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Telecommunications Forum (TELFOR)

Error floor reduction for LDPC codes using self-correction technique

Evgeny A. Likhobabin, Vladimir V. Vityazev

Published Nov 1, 2016• 3 citations
Publisher

Abstract

In this work, we introduce a very simple technique that improves the performance of the belief propagation (BP) and BP-based decoders in waterfall and error-floor regions. Unlike other techniques known in literature, this technique does not explicitly use any trapping sets elimination algorithm, but it modifies the variable node processing by erasing unreliable messages. However, this modification positively affects on the overall decoder performance, and reduces the error floors. At the same time self-correction have insignificant contribution in total computational complexity of LDPC decoder. Moreover it is shown, that such a modification can be used for any BP-based decoding algorithm.

DOI
10.1109/telfor.2016.7818771

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In this work, we introduce a very simple technique that improves the performance of the belief propagation (BP) and BP-based decoders in waterfall and error-floor regions. Unlike other techniques known in literature, this technique does not explicitly use any trapping sets elimination algorithm, but it modifies the variable node processing by erasing unreliable messages. However, this modification positively affects on the overall decoder performance, and reduces the error floors. At the same time self-correction have insignificant contribution in total computational complexity of LDPC decoder. Moreover it is shown, that such a modification can be used for any BP-based decoding algorithm.
In this work, we introduce a unique technique that improves the performance of the BP decoding in waterfall and error-floor regions by reversing the decoder failures. Based on the short cycles existing in the bipartite graph, an importance sampling simulation technique is used to identify the bit and check node combinations that are the dominant sources of error events, called trapping sets. Then, the identified trapping sets are used in the decoding process to avoid the pre-known failures and to converge to the transmitted codeword. With a minimal additional decoding complexity, the proposed technique is able to provide performance improvements for short-length LDPC codes and push or avoid error-floor behaviors of longer codes
In this paper we propose a very simple but powerful self-correction method for the min-sum decoding of LPDC codes. Unlike other correction methods known in the literature, our method does not try to correct the check node processing approximation, but it modifies the variable node processing by erasing unreliable messages. However, this positively affects check node messages, which become symmetric Gaussian distributed, and we show that this is sufficient to ensure a quasi-optimal decoding performance. Monte-Carlo simulations show that the proposed self-corrected min-sum decoding performs very close to the sum-product decoding, while preserving the main features of the min-sum decoding, that is low complexity and independence with respect to noise variance estimation errors.
In this paper, a modified sum-product algorithm to correct bit errors captured within the trapping sets, which are produced in decoding of low-density parity-check (LDPC) codes, is proposed. Unlike the original sum-product algorithm, the proposed decoding method consists of two stages. Whether the main cause of decoding failure is the trapping sets or not is determined at the first stage. And the bit errors within the trapping sets are corrected at the second stage. In the modified algorithm, the set of failed check nodes and the transition patterns of hard-decision bits are exploited to search variable nodes in the trapping sets. After inverting information of the variable nodes, the sum-product algorithm is carried out to correct the bit errors. As a result of simulation, the proposed algorithm shows continuously improved error performance with increase in the signal-to-noise ratio. It is, therefore, considered that the modified sum-product algorithm significantly reduces or possibly eliminates the error floor in LDPC codes.
Trapping sets are considered the primary factor for degrading the performance of low-density parity-check (LDPC) codes in the error-floor region. The effect of trapping sets on the performance of an LDPC code becomes worse as the code size decreases. One approach to tackle this problem is to minimize trapping sets during LDPC code design. However, while trapping sets can be reduced, their complete elimination is infeasible due to the presence of cycles in the underlying LDPC code bipartite graph. In this work, we introduce a new technique based on trapping sets neutralization to minimize the negative effect of trapping sets under belief propagation (BP) decoding. Simulation results for random, progressive edge growth (PEG) and MacKay LDPC codes demonstrate the effectiveness of the proposed technique. The hardware cost of the proposed technique is also shown to be minimal.