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arXiv:2506.20079

Low-Complexity Ordered Reliability Direct Error Pattern Testing (ORDEPT) Decoding with Likelihood Thresholding

Reza Hadavian, Dmitri V. Truhachev

Published Jun 25, 2025• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2506.20079

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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.
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Guessing Random Additive Noise Decoding (GRAND) is a universal framework for decoding all block codes by testing candidate error patterns (EPs). Ordered Reliability Bits GRAND (ORBGRAND) facilitates parallel implementation of GRAND by exploiting log-likelihood ratio (LLR) rankings but still suffers from high tail latency under unfavorable channel conditions, limiting its use in real-time systems. We propose an elimination-aided ORBGRAND scheme that reduces decoding latency by integrating the Rank of the Most Reliable Erroneous (RMRE) bit with a partial Gaussian-elimination (GE) filtering mechanism. The scheme groups and jointly verifies EPs that share the same RMRE, and once a valid EP is identified, the ORBGRAND search is resumed. By leveraging prior GE steps to filter out unnecessary guesses, this approach significantly reduces the number of EPs to be tested, thereby lowering both average and worst-case latency while maintaining error-correction performance. Simulation results show that compared to the original ORBGRAND, the elimination-aided ORBGRAND filters out more than 50\% of EPs and correspondingly reduce overall computational complexity, all with no loss in block error rate. This demonstrates that this approach is suitable for ultra-reliable low-latency communication scenarios.
Ultra-reliable low-latency communications (URLLC) scenario for 6G drives the interest in studying and development of existing and new universal decoding algorithms capable of providing near-optimum error-correcting performance for short block length codes with ultimate goal of providing low latency and moderate complexity. In this paper we consider a new universal decoding technique based on randomized likelihood (RL) rule that may be implemented for practical use in the future. U sing this rule we get the message estimate as a single sample of the message vector from a posterior distribution of messages given the received signal. A soft-decision implementation of RL decoding algorithm is suggested. After suggesting further complexity optimization, the new algorithm is compared to other well-known universal decoders, such as ordered-statistics decoding (OSD) and guessing random additive noise decoding (GRAND). The simulation results for short codes with different rates are provided for binary-input additive white Gaussian noise (BAWGN) communication channel.