Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Guessing What, Noise or Codeword?

Xiao Ma

TL;DR

This work analyzes decoding of binary linear block codes by contrasting guessing codeword decoding (GCD) and guessing noise decoding (GND), and it recasts ordered statistic decoding (OSD) as a specific GCD. It proves that GCD is maximum-likelihood (ML) and requires no more guesses than GND, with termination guaranteed either by exhausting all partial TEPs or via an early-stopping condition based on soft weights, while establishing an injective mapping that bounds the GCD search space by the GND one. The paper then develops several OSD-based variants—LC-OSD, ROSD, and Quasi-OSD—that trade off the online Gaussian-elimination (GE) cost against the number of guesses, and validates these approaches through simulations on BCH, RM, and RS-type codes. Overall, the results show that GCD typically achieves fewer guesses than GND, especially for short, low-rate codes and high-SNR regimes, and that the proposed variants offer practical routes to balance decoding latency, complexity, and performance in URLLC contexts.

Abstract

In this paper, we distinguish two guessing algorithms for decoding binary linear codes. One is the guessing noise decoding (GND) algorithm, and the other is the guessing codeword decoding (GCD) algorithm. We prove that the GCD is a maximum likelihood (ML) decoding algorithm and that the GCD is more efficient than GND for most practical applications. We also introduce several variants of ordered statistic decoding (OSD) to trade off the complexity of the Gaussian elimination (GE) and that of the guessing, which may find applications in decoding short block codes in the high signal-to-noise ratio (SNR) region.

Guessing What, Noise or Codeword?

TL;DR

This work analyzes decoding of binary linear block codes by contrasting guessing codeword decoding (GCD) and guessing noise decoding (GND), and it recasts ordered statistic decoding (OSD) as a specific GCD. It proves that GCD is maximum-likelihood (ML) and requires no more guesses than GND, with termination guaranteed either by exhausting all partial TEPs or via an early-stopping condition based on soft weights, while establishing an injective mapping that bounds the GCD search space by the GND one. The paper then develops several OSD-based variants—LC-OSD, ROSD, and Quasi-OSD—that trade off the online Gaussian-elimination (GE) cost against the number of guesses, and validates these approaches through simulations on BCH, RM, and RS-type codes. Overall, the results show that GCD typically achieves fewer guesses than GND, especially for short, low-rate codes and high-SNR regimes, and that the proposed variants offer practical routes to balance decoding latency, complexity, and performance in URLLC contexts.

Abstract

In this paper, we distinguish two guessing algorithms for decoding binary linear codes. One is the guessing noise decoding (GND) algorithm, and the other is the guessing codeword decoding (GCD) algorithm. We prove that the GCD is a maximum likelihood (ML) decoding algorithm and that the GCD is more efficient than GND for most practical applications. We also introduce several variants of ordered statistic decoding (OSD) to trade off the complexity of the Gaussian elimination (GE) and that of the guessing, which may find applications in decoding short block codes in the high signal-to-noise ratio (SNR) region.
Paper Structure (15 sections, 1 theorem, 10 equations, 4 figures, 2 algorithms)

This paper contains 15 sections, 1 theorem, 10 equations, 4 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. System Model
  4. Guessing Noise Versus Guessing Codeword
  5. The Main Result
  6. The Main Theorem
  7. Illustrative Examples
  8. OSD and Its Variants
  9. A New Perspective on OSD
  10. Variants of OSD
  11. LC-OSD LC_OSD2022LC_OSDljf2023LC_OSDTIT
  12. Representative OSD (ROSD) ROSD
  13. Quasi-OSD QuasiOSD
  14. Simulation Results
  15. Conclusion

Key Result

Theorem 1

The GCD is an ML algorithm, and the number of guessing for the GCD is less than or equal to the number of guessing for the GND.

Figures (4)

  • Figure 1: Average number of guessing for the GND and the GCD. The simulations are conducted for three RM codes over the BPSK-AWGN channels at the target $\text{FER}=10^{-3}$.
  • Figure 2: Simulation results of the eBCH code $\mathscr{C}_{\text{eBCH}}[128,64]$. Here, the maximum number of TEPs $\ell_{\text{max}}=2^{14}$ and $\delta = 8$ for LC-OSD.
  • Figure 3: Simulation results of the RM code $\mathscr{C}_{\text{RM}}[128,64]$. Here, the maximum number of TEPs $\ell_{\text{max}}=10^6$ and $\delta = 12$ for LC-OSD and ROSD.
  • Figure 4: Simulation results of the shortened RS code $\mathscr{C}_{\text{RS}}[26,23]_{2^5}$. Here, the maximum number of TEPs $\ell_{\text{max}}=10^6$ for quasi-OSD, GCD and GND, and $\delta = 8$ for quasi-OSD.

Theorems & Definitions (1)

  • Theorem 1