ORBGRAND Is Almost Capacity-Achieving

TL;DR

This paper demonstrates that ORBGRAND nearly achieves channel capacity for AWGN channels with i.i.d. codebooks and proposes improved finite-length decoding schemes that outperform ORBGRAND at high SNR.

Contribution

It provides an information theoretic analysis of ORBGRAND's capacity-approaching performance and introduces enhanced decoding schemes for finite-length codes.

Findings

Achieves near-capacity rates with ORBGRAND on AWGN channels.

Proposes improved decoding schemes for finite-length codes.

Attains lower error rates than ORBGRAND at high SNR.

Abstract

Decoding via sequentially guessing the error pattern in a received noisy sequence has received attention recently, and ORBGRAND has been proposed as one such decoding algorithm that is capable of utilizing the soft information embedded in the received noisy sequence. An information theoretic study is conducted for ORBGRAND, and it is shown that the achievable rate of ORBGRAND using independent and identically distributed random codebooks almost coincides with the channel capacity, for an additive white Gaussian noise channel under antipodal input. For finite-length codes, improved guessing schemes motivated by the information theoretic study are proposed that attain lower error rates than ORBGRAND, especially in the high signal-to-noise ratio regime.