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Soft-output Guessing Codeword Decoding

Ken R. Duffy, Peihong Yuan, Joseph Griffin, Muriel Medard

TL;DR

The paper addresses obtaining accurate soft-output from Guessing Codeword Decoding (GCD) by framing GCD as a variant of GRAND and deriving efficient blockwise and bitwise soft-output measures with minimal extra computation. It provides formulations (SOGRAND-style) and validates them on random linear codes and eBCH codes, showing that a Lambda parameter of at least 2 yields high-fidelity soft information. The authors demonstrate the use of SO-GCD-ORB within SISO decoding of product codes, achieving performance comparable to SOGRAND with substantially lower decoding effort. These results enable reliable ARQ decisions and efficient iterative decoding for long, high-redundancy codes, with favorable hardware implications compatible with 1-line ORBGRAND ordering.

Abstract

We establish that it is possible to extract accurate blockwise and bitwise soft output from Guessing Codeword Decoding with minimal additional computational complexity by considering it as a variant of Guessing Random Additive Noise Decoding. Blockwise soft output can be used to control decoding misdetection rate while bitwise soft output results in a soft-input soft-output decoder that can be used for efficient iterative decoding of long, high redundancy codes.

Soft-output Guessing Codeword Decoding

TL;DR

The paper addresses obtaining accurate soft-output from Guessing Codeword Decoding (GCD) by framing GCD as a variant of GRAND and deriving efficient blockwise and bitwise soft-output measures with minimal extra computation. It provides formulations (SOGRAND-style) and validates them on random linear codes and eBCH codes, showing that a Lambda parameter of at least 2 yields high-fidelity soft information. The authors demonstrate the use of SO-GCD-ORB within SISO decoding of product codes, achieving performance comparable to SOGRAND with substantially lower decoding effort. These results enable reliable ARQ decisions and efficient iterative decoding for long, high-redundancy codes, with favorable hardware implications compatible with 1-line ORBGRAND ordering.

Abstract

We establish that it is possible to extract accurate blockwise and bitwise soft output from Guessing Codeword Decoding with minimal additional computational complexity by considering it as a variant of Guessing Random Additive Noise Decoding. Blockwise soft output can be used to control decoding misdetection rate while bitwise soft output results in a soft-input soft-output decoder that can be used for efficient iterative decoding of long, high redundancy codes.
Paper Structure (7 sections, 8 equations, 4 figures)

This paper contains 7 sections, 8 equations, 4 figures.

Table of Contents

  1. Introduction
  2. GRAND and SO
  3. GCD and SO
  4. Noise effect sequences
  5. SO-GCD accuracy
  6. SISO Decoding
  7. Discussion

Figures (4)

  • Figure 1: SO Predicted BLER vs. empirical BLER: RLCs, SO-GCD-ORB, $E_b/N_0=3$.
  • Figure 2: SO Predicted BLER vs. empirical BLER: eBCH codes, SO-GCD-ORB, $E_b/N_0=3$.
  • Figure 3: SO Predicted BER vs. empirical BER: eBCH codes, SO-GCD-ORB, $E_b/N_0=3$.
  • Figure 4: Turbo product code decoding with SO-GCD-ORB. For eBCH product codes of dimensions $(256,121)$, $(1024,676)$ and $(4096,3249)$, the upper panel shows block (solid) and bit (dashed) error rate as well as achievability bounds. The lower panel shows the average number of guesses until the decoding terminates.