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.

翻译：本文针对噪声信道下(n,k)线性分组码校验矩阵的盲恢复问题，提出了一种由三部分组成的快速恢复方案。首先，该方案在接收码字中执行初始错误位置检测，并筛选出可靠的码字。其次，通过高斯消元法处理k×k满秩矩阵，结合阈值与可靠性验证机制对恢复出的对偶字进行校验，以提升恢复可靠性。最后，利用部分恢复的对偶字对接收码字进行译码。这三个部分可根据不同噪声场景组合成多种方案。其中，结合高斯消元与验证的GEV方案比基于n×n满秩矩阵高斯消元的现有Canteaut-Chabaud算法具有显著更低的恢复失败概率和计算复杂度。针对高噪声场景，译码辅助恢复方案与错误检测-码字选择-译码辅助恢复方案在提升码恢复性能方面优于GEV，且其计算复杂度仍远低于基于Canteaut-Chabaud的算法。