A branch-cut-and-price algorithm for optimal decoding in digital communication systems

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.