Fast Blind Recovery of Linear Block Codes over Noisy Channels

This paper addresses the blind recovery of the parity check matrix of an (n, k) linear block code over noisy channels by proposing a fast recovery scheme consisting of 3 parts. Firstly, this scheme performs initial error position detection among the received codewords and selects the desirable codewords. Then, this scheme conducts Gaussian elimination (GE) on a k-by-k full-rank matrix and uses a threshold and the reliability associated to verify the recovered dual words, aiming to improve the reliability of recovery. Finally, it performs decoding on the received codewords with partially recovered dual words. These three parts can be combined into different schemes for different noise level scenarios. The GEV that combines Gaussian elimination and verification has a significantly lower recovery failure probability and a much lower computational complexity than an existing Canteaut-Chabaud-based algorithm, which relies on GE on n-by-n full-rank matrices. The decoding-aided recovery (DAR) and error-detection-&-codeword-selection-&-decoding-aided recovery (EDCSDAR) schemes can improve the code recovery performance over GEV for high noise level scenarios, and their computational complexities remain much lower than the Canteaut-Chabaud-based algorithm.