Channel coding aims to minimize the errors that occur during the transmission of digital information from one place to another. Low-density parity-check codes can detect and correct transmission errors if one encodes the original information by adding redundant bits. In practice, heuristic iterative decoding algorithms are used to decode the received vector. However, these algorithms may fail to decode if the received vector contains multiple errors. We consider decoding the received vector with minimum error as an integer programming (IP) problem and propose a branch-and-price method for its solution. We improve the performance of our method by introducing heuristic feasible solutions and adding valid cuts to the mathematical formulation. Our computational experiments reveal that our branch-cut-and-price algorithm significantly improves solvability of the problem compared to a state-of-the-art IP decoder in the literature and has superior error performance than the conventional sum-product algorithm.

信道编码旨在最大限度地减少数字信息从一个地方传输到另一个地方的过程中出现的错误。如果通过添加冗余位对原始信息进行编码，低密度奇偶校验码可以检测和纠正传输错误。在实践中，启发式迭代解码算法用于解码接收到的向量。但是，如果接收到的向量包含多个错误，这些算法可能无法解码。我们考虑将接收到的向量以最小错误解码为整数规划 (IP) 问题，并为其解决方案提出了分支和价格方法。我们通过引入启发式可行解决方案并在数学公式中添加有效切割来提高我们方法的性能。