Parity Check Matrix Recognition from Noisy Codewords

TL;DR

This paper presents a low-complexity iterative algorithm for recovering parity check matrices from noisy codewords received over a Binary Symmetric Channel, enabling effective decoding even at high noise levels.

Contribution

The paper introduces a practical, XOR-based iterative column elimination algorithm for parity check matrix recovery from noisy data, with low computational complexity and robustness to noise.

Findings

Algorithm successfully recovers parity check matrices at high noise levels.

Low computational complexity enables code length and synchronization searches.

Experimental results validate the effectiveness of the proposed method.

Abstract

We study recovering parity check relations for an unknown code from intercepted bitstream received from Binary Symmetric Channel in this paper. An iterative column elimination algorithm is introduced which attempts to eliminate parity bits in codewords of noisy data. This algorithm is very practical due to low complexity and use of XOR operator. Since, the computational complexity is low, searching for the length of code and synchronization is possible. Furthermore, the Hamming weight of the parity check words are only used in threshold computation and unlike other algorithms, they have negligible effect in the proposed algorithm. Eventually, experimental results are presented and estimations for the maximum noise level allowed for recovering the words of the parity check matrix are investigated.