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Ordered Reliability Direct Error Pattern Testing Decoding Algorithm

Reza Hadavian, Xiaoting Huang, Dmitri V. Truhachev, Kamal El‐Sankary, Hamid Ebrahimzad, Hossein Najafi

Published Oct 18, 2023• 0 citations
Publisher

Abstract

We propose a new decoding algorithm for binary codes called ordered reliability direct error pattern testing (ORDEPT) which is based on completion of partial error patterns arranged in the order of likelihood. Based on ORDEPT we proposed a new adaptive-hybrid algorithm for decoding of product codes. The proposed algorithms outperform state-of-the-art decoders on various metrics for a variety of single and product-like codes.

DOI
10.36227/techrxiv.24328879

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IEEE Transactions on Information Theory•Jan 23, 2007•60 citations
We propose a new decoding algorithm for binary codes called ordered reliability direct error pattern testing (ORDEPT) which is based on completion of partial error patterns arranged in the order of likelihood. Based on ORDEPT we proposed a new adaptive-hybrid algorithm for decoding of product codes. The proposed algorithms outperform state-of-the-art decoders on various metrics for a variety of single and product-like codes.
We introduce a novel soft-decision decoding algorithm for binary block codes named ordered reliability direct error pattern testing (ORDEPT). The proposed technique tests a list of partial error patterns (PEP)s that are arranged according to their logistic weight and completed on-the-fly based on the instantaneous received sequence and the code’s parity-check matrix. Our results, obtained for a variety of popular short high-rate codes, demonstrate that ORDEPT outperforms state-of-the-art decoding algorithms such as ordered reliability bits guessing random additive noise decoding (ORBGRAND) in terms of decoding complexity, and is hardware-favorable in terms of latency and energy consumption. The improvements carry on to the iterative decoding of product codes and convolutional product-like codes, where ORDEPT demonstrates the ability to efficiently find multiple candidate codewords and outperform state-of-the art competitors.
We introduce a novel universal soft-decision decoding algorithm for binary block codes called ordered reliability direct error pattern testing (ORDEPT). Our results, obtained for a variety of popular short high-rate codes, demonstrate that ORDEPT outperforms state-of-the-art decoding algorithms of comparable complexity such as ordered reliability bits guessing random additive noise decoding (ORBGRAND) in terms of the decoding error probability and latency. The improvements carry on to the iterative decoding of product codes and convolutional product-like codes, where we present a new adaptive decoding algorithm and demonstrate the ability of ORDEPT to efficiently find multiple candidate codewords to produce soft output.
In this work we introduce a novel soft-decision decoding algorithm for high-rate short error-correction codes. Our results demonstrate that the proposed algorithm improves over the state-of-the-art algorithms, including recently proposed Ordered Reliability Bits Guessing Random Additive Noise Decoding (ORBGRAND), in terms of latency and decoding complexity. Specifically, we demonstrate that the ability of the proposed algorithm to find multiple candidate codewords with a reduced number of low-complexity queries makes it an efficient component decoder for iterative decoding of product-like codes.
We propose a reduced complexity approach to pattern-based soft decoding of block codes. We start from the ORDEPT decoding algorithm which tests a list of partial error patterns organized in the order of their likelihood and attempts to complete the patterns creating candidate codewords. We then propose an early termination criterion. Once a candidate codeword is found, its log-likelihood difference to the received sequence is compared to a preset threshold and the decoding decision is instantly made in case the likelihood deviation is below the threshold. We demonstrate that while keeping the same block error rate (BLER) performance, the proposed algorithm's latency and complexity is multiple times smaller than that of the state-of-the art competitors including the Chase II, ORBGRAND, GCD, and the very recent ORDEPT with Soft-Output GRAND termination which necessitates several multiplications in each query processing.
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.
This correspondence investigates soft-decision decoding of binary linear block codes using ordered recodings of test error patterns on the so-called "most reliable basis." The analysis demonstrates the optimality of the most reliable basis by showing that, among all possible bases, the most reliable basis minimizes the list error probability for a very general (and well-defined) class of orderings for recoding operations. The correspondence then proposes a suboptimal algorithm which utilizes reprocessing ordering and incorporates two techniques that render it computationally very efficient: 1) an iterative reference recoding technique which simplifies the recoding operation required for each test error pattern, and 2) an adaptive skipping rule which significantly reduces the average number of recodings. Simulation results with codes of relatively large length show that the proposed algorithm is computationally very efficient in comparison to existing algorithms in the literature