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Approaching Maximum Likelihood Decoding Performance via Reshuffling ORBGRAND

Li Wan, Wenyi Zhang

TL;DR

This work targets the decoding of short, high-rate block codes using the GRAND framework, where ORBGRAND offers hardware-friendly querying based on LLR magnitudes but incurs a block-error-rate gap to maximum likelihood (ML) decoding. The authors propose RS-ORBGRAND, an offline reshuffling of ORBGRAND’s query order guided by a search-problem analysis that minimizes the expected number of queries, effectively approximating SGRAND while preserving ORB-type structure. They derive a monotonicity property for the ensemble-averaged posterior terms and demonstrate that RS-ORBGRAND achieves substantial gains over existing ORB-type methods, approaching ML performance within $0.1$ dB at a BLER of $10^{-6}$ on BCH and polar codes. The method preserves hardware efficiency and is well-suited for URLLC scenarios, offering near-ML decoding performance with practical query costs.

Abstract

Guessing random additive noise decoding (GRAND) is a recently proposed decoding paradigm particularly suitable for codes with short length and high rate. Among its variants, ordered reliability bits GRAND (ORBGRAND) exploits soft information in a simple and effective fashion to schedule its queries, thereby allowing efficient hardware implementation. Compared with maximum likelihood (ML) decoding, however, ORBGRAND still exhibits noticeable performance loss in terms of block error rate (BLER). In order to improve the performance of ORBGRAND while still retaining its amenability to hardware implementation, a new variant of ORBGRAND termed RS-ORBGRAND is proposed, whose basic idea is to reshuffle the queries of ORBGRAND so that the expected number of queries is minimized. Numerical simulations show that RS-ORBGRAND leads to noticeable gains compared with ORBGRAND and its existing variants, and is only 0.1dB away from ML decoding, for BLER as low as $10^{-6}$.

Approaching Maximum Likelihood Decoding Performance via Reshuffling ORBGRAND

TL;DR

This work targets the decoding of short, high-rate block codes using the GRAND framework, where ORBGRAND offers hardware-friendly querying based on LLR magnitudes but incurs a block-error-rate gap to maximum likelihood (ML) decoding. The authors propose RS-ORBGRAND, an offline reshuffling of ORBGRAND’s query order guided by a search-problem analysis that minimizes the expected number of queries, effectively approximating SGRAND while preserving ORB-type structure. They derive a monotonicity property for the ensemble-averaged posterior terms and demonstrate that RS-ORBGRAND achieves substantial gains over existing ORB-type methods, approaching ML performance within dB at a BLER of on BCH and polar codes. The method preserves hardware efficiency and is well-suited for URLLC scenarios, offering near-ML decoding performance with practical query costs.

Abstract

Guessing random additive noise decoding (GRAND) is a recently proposed decoding paradigm particularly suitable for codes with short length and high rate. Among its variants, ordered reliability bits GRAND (ORBGRAND) exploits soft information in a simple and effective fashion to schedule its queries, thereby allowing efficient hardware implementation. Compared with maximum likelihood (ML) decoding, however, ORBGRAND still exhibits noticeable performance loss in terms of block error rate (BLER). In order to improve the performance of ORBGRAND while still retaining its amenability to hardware implementation, a new variant of ORBGRAND termed RS-ORBGRAND is proposed, whose basic idea is to reshuffle the queries of ORBGRAND so that the expected number of queries is minimized. Numerical simulations show that RS-ORBGRAND leads to noticeable gains compared with ORBGRAND and its existing variants, and is only 0.1dB away from ML decoding, for BLER as low as .
Paper Structure (10 sections, 5 theorems, 16 equations, 3 figures, 1 table)

This paper contains 10 sections, 5 theorems, 16 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Channel Model
  4. GRAND
  5. Search Problem and Reshuffled Querying
  6. Search Problem Formulation
  7. Analysis of Search Problem
  8. Reshuffled Querying
  9. Performance Evaluation
  10. Conclusion

Key Result

Theorem 1

For the search problem in Section Question setting, the expected number of queries before the searcher stops is given by where conditioned upon $\underline{Y} = \underline{y}$, $S_t$ is realized as in which the subscript $\underline{W}|\underline{Y}$ emphasizes that $s_t$ is the posterior probability that the codeword is $\theta(\underline{Y}) \oplus \underline{e}(\pi(t))$ when the searcher obse

Figures (3)

  • Figure 1: Illustration of $\mathcal{R}$ before and after applying the reshuffling step.
  • Figure 2: BLER for BCH(127, 113).
  • Figure 3: BLER for CRC-aided Polar(128, 114).

Theorems & Definitions (5)

  • Theorem 1
  • Lemma 1
  • Corollary 1
  • Proposition 1
  • Proposition 2