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arXiv:1901.02603 · Globecom

Segmentation-Discarding Ordered-Statistic Decoding for Linear Block Codes

Chentao Yue, Mahyar Shirvanimoghaddam, Yonghui Li, Branka S. Vucetic

Published Dec 1, 2019• 42 citations
arXivHTMLPDF

Abstract

In this paper, we propose an efficient reliability based segmentation-discarding decoding (SDD) algorithm for short block-length codes. A novel segmentation- discarding technique is proposed along with the stopping rule to significantly reduce the decoding complexity without a significant performance degradation compared to ordered statistics decoding (OSD). In the proposed decoder, the list of test error patterns (TEPs) is divided into several segments according to carefully selected boundaries and every segment is checked separately during the reprocessing stage. Decoding is performed under the constraint of the discarding rule and stopping rule. Simulations results for different codes show that our proposed algorithm can significantly reduce the decoding complexity compared to the existing OSD algorithms in literature.

DOI
10.1109/globecom38437.2019.9014173

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In this paper, we propose an efficient reliability based segmentation-discarding decoding (SDD) algorithm for short block-length codes. A novel segmentation- discarding technique is proposed along with the stopping rule to significantly reduce the decoding complexity without a significant performance degradation compared to ordered statistics decoding (OSD). In the proposed decoder, the list of test error patterns (TEPs) is divided into several segments according to carefully selected boundaries and every segment is checked separately during the reprocessing stage. Decoding is performed under the constraint of the discarding rule and stopping rule. Simulations results for different codes show that our proposed algorithm can significantly reduce the decoding complexity compared to the existing OSD algorithms in literature.
This letter proposes an efficient probability-based ordered-statistics decoding (PB-OSD) algorithm for short block-length codes. In PB-OSD, we derive two probabilistic measures on the codeword estimates and test error patterns, respectively referred to as the success probability and promising probability. Based on these probabilities, a stopping criterion and a discarding criterion are developed to reduce the number of test error patterns and limit the decoding complexity. To further reduce the complexity, we propose a tree-based search strategy to find the most likely test error patterns in reprocessing stage of the OSD algorithm. Simulation results show that PB-OSD significantly reduces the decoding complexity under the same error performance, compared to the original OSD algorithm.
The ordered statistics-based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of a list of the test error patterns is considered. The original ordered-statistics decoding (OSD) is generalized by assuming segmentation of the most reliable independent positions (MRIPs) of the received bits. The segmentation is shown to overcome several drawbacks of the original OSD. The complexity of the ordered statistics-based decoding is further reduced by assuming a partial ordering of the received bits in order to avoid the complex Gauss elimination. The probability of the test error patterns in the decoding list is derived. The bit error rate performance and the decoding complexity trade-off of the proposed decoding algorithms is studied by computer simulations. Numerical examples show that, in some cases, the proposed decoding schemes are superior to the original OSD in terms of both the bit error rate performance as well as the decoding complexity.
The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics decoding is generalized by assuming segmentation of the most reliable independent positions of the received bits. The segmentation is shown to overcome several drawbacks of the original order statistics decoding. The complexity of the order statistics based decoding is further reduced by assuming a partial ordering of the received bits in order to avoid the complex Gauss elimination. The probability of the test error patterns in the decoding list is derived. The bit error rate performance and the decoding complexity trade-off of the proposed decoding algorithms is studied by computer simulations. Numerical examples show that, in some cases, the proposed decoding schemes are superior to the original order statistics decoding in terms of both the bit error rate performance as well as the decoding complexity.
This letter is concerned with a generalized ordered statistic decoding (OSD) algorithm, called locally constrained OSD (LC-OSD). Instead of order-tttreprocessing on the most reliable independent bits, the LC-OSD searches for test error patterns using the serial list Viterbi algorithm (SLVA) over a trellis specified by a local parity-check matrix. We derive several early stopping criteria that can be used to reduce the number of searches. Numerical results show that the LC-OSD algorithm with the proposed stopping criteria has much lower time complexity than the original OSD but incurs negligible performance loss.
In this paper, we propose an efficient decoding algorithm for short low-density parity check (LDPC) codes by carefully combining the belief propagation (BP) decoding and ordered statistics decoding (OSD) algorithms. Specifically, a modified BP (mBP) algorithm is applied for a certain number of iterations prior to OSD to enhance the reliability of the received message, where an offset parameter is utilized in mBP to control the weight of the extrinsic information in message passing. By carefully selecting the offset parameter and the number of mBP iterations, the number of errors in the most reliable positions (MRPs) in OSD can be reduced by mBP, thereby significantly improving the overall decoding performance of error rate and complexity. Simulation results show that the proposed algorithm can approach the maximum-likelihood decoding (MLD) for short LDPC codes with only a slight increase in complexity compared to BP and a significant decrease compared to OSD. Specifically, the order- (m -1) decoding of the proposed algorithm can achieve the performance of the order-m OSD.
Aiming at bridge gap between maximum likelihood decoding (MLD) and belief propagation (BP) decoding for short or medium LDPC codes, we present one modified ordered statistics decoding (OSD) reprocessing method, which is serially concatenated with standard BP. Meanwhile, two novel points in implementation are addressed. For one thing, the new definition of bit reliability proposed enhances error-correcting performance via centralizing more decoding errors of standard BP within the scope of order-p OSD where p ≤ 2. For another, one way of reducing computational complexity is put forward in selecting optimal error pattern among all candidates. Simulation results demonstrate our approach could achieve good tradeoff between reprocessing performance and computational complexity. Techniques on further improvement are also discussed briefly. Reliability-based syndrome decoding of LDPC codes 1 I.