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Blind Identification of Channel Codes: A Subspace-Coding Approach

Pramod Singh, Prasad Krishnan, Arti Yardi

TL;DR

This work addresses blind identification of channel codes on the binary symmetric channel by introducing a subspace-coding perspective. It develops the minimum denoised subspace discrepancy (M-DenSD) decoder, which denoises received rows via bounded-distance decoding and then uses a subspace-distance criterion to identify the transmitted code; an improved ISD variant handles large N by operating on a selected subset of rows. The authors provide rigorous guarantees under rank and low-weight-error conditions, derive an analytical bound on the error probability for the improved decoder, and demonstrate experimentally that the proposed method outperforms existing general-purpose techniques for random linear codes, especially with limited observations and higher noise. Overall, the paper bridges subspace coding and blind code-identification to enable analysis and practical decoding for general code families with potential extensions to other channels and identification tasks.

Abstract

The problem of blind identification of channel codes at a receiver involves identifying a code chosen by a transmitter from a known code-family, by observing the transmitted codewords through the channel. Most existing approaches for code-identification are contingent upon the codes in the family having some special structure, and are often computationally expensive otherwise. Further, rigorous analytical guarantees on the performance of these existing techniques are largely absent. This work presents a new method for code-identification on the binary symmetric channel (BSC), inspired by the framework of subspace codes for operator channels, carefully combining principles of hamming-metric and subspace-metric decoding. We refer to this method as the minimum denoised subspace discrepancy decoder. We present theoretical guarantees for code-identification using this decoder, for bounded-weight errors, and also present a bound on the probability of error when used on the BSC. Simulations demonstrate the improved performance of our decoder for random linear codes beyond existing general-purpose techniques, across most channel conditions and even with a limited number of received vectors.

Blind Identification of Channel Codes: A Subspace-Coding Approach

TL;DR

This work addresses blind identification of channel codes on the binary symmetric channel by introducing a subspace-coding perspective. It develops the minimum denoised subspace discrepancy (M-DenSD) decoder, which denoises received rows via bounded-distance decoding and then uses a subspace-distance criterion to identify the transmitted code; an improved ISD variant handles large N by operating on a selected subset of rows. The authors provide rigorous guarantees under rank and low-weight-error conditions, derive an analytical bound on the error probability for the improved decoder, and demonstrate experimentally that the proposed method outperforms existing general-purpose techniques for random linear codes, especially with limited observations and higher noise. Overall, the paper bridges subspace coding and blind code-identification to enable analysis and practical decoding for general code families with potential extensions to other channels and identification tasks.

Abstract

The problem of blind identification of channel codes at a receiver involves identifying a code chosen by a transmitter from a known code-family, by observing the transmitted codewords through the channel. Most existing approaches for code-identification are contingent upon the codes in the family having some special structure, and are often computationally expensive otherwise. Further, rigorous analytical guarantees on the performance of these existing techniques are largely absent. This work presents a new method for code-identification on the binary symmetric channel (BSC), inspired by the framework of subspace codes for operator channels, carefully combining principles of hamming-metric and subspace-metric decoding. We refer to this method as the minimum denoised subspace discrepancy decoder. We present theoretical guarantees for code-identification using this decoder, for bounded-weight errors, and also present a bound on the probability of error when used on the BSC. Simulations demonstrate the improved performance of our decoder for random linear codes beyond existing general-purpose techniques, across most channel conditions and even with a limited number of received vectors.
Paper Structure (10 sections, 4 theorems, 17 equations, 5 figures, 1 algorithm)

This paper contains 10 sections, 4 theorems, 17 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Preliminaries
  3. Code-Identification: Literature Review
  4. Relation to Subspace Codes
  5. A New Decoder for code-identification
  6. Guaranteed Identification Capabilities of the $\mathsf{M}\text{-}\mathsf{DenSD}$ decoder
  7. An Improved Decoder for Large $N$
  8. Bound on the Error Probability of Improved $\mathsf{M}\text{-}\mathsf{DenSD}$ Decoder
  9. Simulation Results
  10. Conclusion and Future Work

Key Result

Theorem 1

silva_ksishch_RankmetricApproach For the channel model $Y = AX + BZ$, let $X$ be chosen at random from the collection of generator matrices of a subspace code $\mathfrak{S}$ with minimum subspace distance $d^{\mathsf{sub}}$ and $Y$. For some $\rho\geq 0$, suppose $\mathsf{rank}(A) \ge \max_{{\cal S}

Figures (5)

  • Figure 1: Code Identification on BSC$(p)$
  • Figure 2: Performance of $\mathsf{M}\text{-}\mathsf{DenSD}$ decoder indicating the worsening of performance for $N$ beyond some threshold $N^*$ (in this case, $N^*\approx 20$)
  • Figure 3: Performance comparison: Improved $\mathsf{M}\text{-}\mathsf{DenSD}$, Inner-Product Method, and MSD decoders ($n= 30, k =10, k_{1,2}=5$)
  • Figure 4: Error probability of Improved $\mathsf{M}\text{-}\mathsf{DenSD}$ decoder.
  • Figure 5: Performance of Improved $\mathsf{M}\text{-}\mathsf{DenSD}$ Decoder for different code parameters.

Theorems & Definitions (8)

  • Theorem 1
  • Remark 1
  • Definition 1
  • Theorem 2
  • Corollary 1
  • Remark 2
  • Theorem 3
  • Remark 3