Blind Identification of Channel Codes: A Subspace-Coding Approach

TL;DR

This paper introduces a novel subspace-coding based method for blind identification of channel codes over the BSC, providing theoretical guarantees and demonstrating improved performance over existing techniques.

Contribution

It proposes the minimum denoised subspace discrepancy decoder, a new approach combining hamming and subspace metrics with theoretical error bounds.

Findings

The decoder offers improved code-identification accuracy over existing methods.

Theoretical guarantees are established for bounded-weight errors.

Simulations show superior performance on random linear codes across various channel conditions.

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.