Guessing Decoding of Short Blocklength Codes

TL;DR

This paper unifies and analyzes guessing decoding methods like GRAND and GCD for short blocklength codes, providing theoretical insights, optimality proofs, and practical guidelines for ultra-reliable low-latency communication systems.

Contribution

It offers a unified framework for guessing decoding, proves ML optimality, derives approximations, and compares performance metrics of GRAND and GCD.

Findings

Grand and GCD are optimal under certain stopping criteria.

Theoretical predictions match simulation results.

Performance regimes where each method excels are identified.

Abstract

Future beyond-5G and 6G systems demand ultra-reliable, low-latency communication with short blocklengths, motivating the development of universal decoding algorithms. Guessing decoding, which infers the noise or codeword candidate in order of decreasing (exact or approximate) likelihood, offers a universal framework applicable to short codes. In this paper, we present a unified treatment of two prominent recent families of guessing decoding: guessing random additive noise decoding (GRAND) and guessing codeword decoding (GCD). For each, we (i) present algorithmic implementations and ordering strategies; (ii) prove maximum-likelihood (ML) optimality under appropriate stopping criteria; (iii) derive saddle-point approximations for the average number of queries; and (iv) validate theoretical predictions with simulations. We further analyze the performance degradation due to limited search budgets relative to ML performance, compare key metrics (worst-case and average complexity, hardware considerations), and highlight how advances in one approach transfer naturally to the other. Our results clarify the operating regimes where GRAND and GCD demonstrate superior performance. This work provides both theoretical insights and practical guidelines for deploying universal guessing decoders in next-generation short-blocklength communications.