Ordered Reliability Bits Guessing Random Additive Noise Decoding

Abstract

Error correction techniques traditionally focus on the co-design of restricted code-structures in tandem with codespecific decoders that are computationally efficient when decoding long codes in hardware. Modern applications are, however, driving demand for ultra-reliable low-latency communications (URLLC), rekindling interest in the performance of shorter, higher-rate error correcting codes, and raising the possibility of revisiting universal, code-agnostic decoders.To that end, here we introduce a soft-detection variant of Guessing Random Additive Noise Decoding (GRAND) called Ordered Reliability Bits GRAND that can accurately decode any moderate redundancy block-code. It is designed with efficient circuit implementation in mind, and determines accurate decodings while retaining the original hard detection GRAND algorithm's suitability for a highly parallelized implementation in hardware.ORBGRAND is shown to provide excellent soft decision block error performance for codes of distinct classes (BCH, CA-Polar and RLC) with modest complexity, while providing better block error rate performance than CA-SCL, a state of the art soft detection CA-Polar decoder. ORBGRAND offers the possibility of an accurate, energy efficient soft detection decoder suitable for delivering URLLC in a single hardware realization.

Block turbo decoding with ORBGRAND

“…Both hard-input and soft-input variants of GRAND exist. Of interest here is ORBGRAND [6,7,23,24], a soft-input GRAND variant that offers a balance between accuracy and complexity, and that has been the subject of efficient, high-throughput hardware designs [10,13].…”

“…The full ORBGRAND algorithm [7] details how to generate putative noise sequences in order of their total weight, which is an approximation of their maximum-likelihood order. We detail a simple method in section III-C, and also describe a simple method to find a suitable value for c.…”

“…In Algorithm 2, we present a simple method to construct the noise sequences for 1-line ORBGRAND that has similar implementation complexity as basic ORBGRAND. The noise sequences are generated in order of their total weight, w T = 0, 1, 2, .... For each value of w T , we iterate over all valid pairs of non-negative integers (w H , w L ) such that w T = cw H +w L , and the landslide algorithm [7] generates all noise sequences for each pair.…”

“…GRAND is a recently introduced family of hard [1][2][3] and soft [4][5][6][7] decoding algorithms that can accurately decode arbritrary codes, even non-linear ones [8], with a moderate number of redundant bits. Their promise for practical, highlyparallelised decoding has led to the publication of several circuit designs and a chip implementation [9][10][11][12][13].…”

“…The decoding list produced by GRAND can be used to update the bit reliabilities as before, with the benefit that GRAND's code-agnosticism allows it to turbo decode any product code. We present empirical results for block turbo decoding with Ordered Reliability Bits GRAND (ORBGRAND) [6,7], a softinput variant of GRAND that is particularly suited to hardware implementation [10,13]. We also provide general analytical support for list decoding with all GRAND algorithms and consider the performance of ORBGRAND as a standalone list decoder.…”