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ORBGRAND: Achievable Rate for General Bit Channels and Application in BICM

Zhuang Li, Wenyi Zhang

TL;DR

This work extends ORBGRAND from AWGN to general memoryless binary-input bit channels by deriving its generalized mutual information (GMI) as the achievable rate, using a first-principles analysis that accounts for the ranking-induced correlation of error patterns. It provides an explicit I_ORBGRAND formula that quantifies how closely ORBGRAND can approach the channel mutual information, and explains the gap via the nonlinear transformation Ψ of the log-likelihood ratios. As an application, the authors analyze the ORBGRAND achievable rate for bit-interleaved coded modulation (BICM) and show through numerical results on QPSK, 8PSK, and 16QAM (Gray and set-partitioning labelings) over AWGN and Rayleigh channels that the gap to I is small, particularly in AWGN. The findings indicate ORBGRAND is both near-optimal and hardware-friendly for high-order coded modulation schemes, supporting its feasibility for practical, high-rate transmission systems.

Abstract

Guessing random additive noise decoding (GRAND) has received widespread attention recently, and among its variants, ordered reliability bits GRAND (ORBGRAND) is particularly attractive due to its efficient utilization of soft information and its amenability to hardware implementation. It has been recently shown that ORBGRAND is almost capacity-achieving in additive white Gaussian noise channels under antipodal input. In this work, we first extend the analysis of ORBGRAND achievable rate to memoryless binary-input bit channels with general output conditional probability distributions. The analytical result also sheds insight into understanding the gap between the ORBGRAND achievable rate and the channel mutual information. As an application of the analysis, we study the ORBGRAND achievable rate of bit-interleaved coded modulation (BICM). Numerical results indicate that for BICM, the gap between the ORBGRAND achievable rate and the channel mutual information is typically small, and hence suggest the feasibility of ORBGRAND for channels with high-order coded modulation schemes.

ORBGRAND: Achievable Rate for General Bit Channels and Application in BICM

TL;DR

This work extends ORBGRAND from AWGN to general memoryless binary-input bit channels by deriving its generalized mutual information (GMI) as the achievable rate, using a first-principles analysis that accounts for the ranking-induced correlation of error patterns. It provides an explicit I_ORBGRAND formula that quantifies how closely ORBGRAND can approach the channel mutual information, and explains the gap via the nonlinear transformation Ψ of the log-likelihood ratios. As an application, the authors analyze the ORBGRAND achievable rate for bit-interleaved coded modulation (BICM) and show through numerical results on QPSK, 8PSK, and 16QAM (Gray and set-partitioning labelings) over AWGN and Rayleigh channels that the gap to I is small, particularly in AWGN. The findings indicate ORBGRAND is both near-optimal and hardware-friendly for high-order coded modulation schemes, supporting its feasibility for practical, high-rate transmission systems.

Abstract

Guessing random additive noise decoding (GRAND) has received widespread attention recently, and among its variants, ordered reliability bits GRAND (ORBGRAND) is particularly attractive due to its efficient utilization of soft information and its amenability to hardware implementation. It has been recently shown that ORBGRAND is almost capacity-achieving in additive white Gaussian noise channels under antipodal input. In this work, we first extend the analysis of ORBGRAND achievable rate to memoryless binary-input bit channels with general output conditional probability distributions. The analytical result also sheds insight into understanding the gap between the ORBGRAND achievable rate and the channel mutual information. As an application of the analysis, we study the ORBGRAND achievable rate of bit-interleaved coded modulation (BICM). Numerical results indicate that for BICM, the gap between the ORBGRAND achievable rate and the channel mutual information is typically small, and hence suggest the feasibility of ORBGRAND for channels with high-order coded modulation schemes.
Paper Structure (14 sections, 5 theorems, 31 equations, 8 figures)

This paper contains 14 sections, 5 theorems, 31 equations, 8 figures.

Table of Contents

  1. Introduction
  2. System Model and ORBGRAND for General Bit Channels
  3. System Model
  4. ORBGRAND for General Bit Channels
  5. GMI Analysis of ORBGRAND
  6. GMI of ORBGRAND
  7. Discussion on Gap between GMI of ORBGRAND and Channel Mutual Information
  8. Application in BICM
  9. Experimental Setup
  10. Numerical Results
  11. Conclusion
  12. Proof of Lemma 1
  13. Proof of Lemma 2
  14. Proof of Lemma 3

Key Result

Theorem 1

For the system setup in Section system model, the GMI of ORBGRAND is given by in nats/channel use.

Figures (8)

  • Figure 1: Plots of $\Psi(t)$ under under AWGN and Rayleigh fading channels.
  • Figure 2: Plots of $I_{\text{ORBGRAND}}$ and $I$ under AWGN and Rayleigh fading channels.
  • Figure 3: Gray (left) and set-partitioning (right) labelings for 16QAM.
  • Figure 4: Parallel channel model of BICM with ideal interleaving.
  • Figure 5: ORBGRAND achievable rate and channel mutual information under QPSK, 8PSK and 16QAM for AWGN channel in the case of Gray labeling.
  • ...and 3 more figures

Theorems & Definitions (5)

  • Theorem 1
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Proposition 1