A Branch-Price-and-Cut Algorithm for Optimal Decoding of LDPC Codes

Abstract

Channel coding aims to minimize errors that occur during the transmission of digital information from one place to another. Low-density parity-check (LDPC) 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 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. Computational results reveal that our branch-priceand-cut algorithm significantly improves solvability of the problem compared to a commercial solver in high channel error rates. Our proposed algorithm can find higher quality solutions than commonly used iterative decoding heuristics.

Cardinality Minimization, Constraints, and Regularization: A Survey

“…[275], and it is also important in other fields, e.g., in the context of tensor decompositions [219,215,353] (by relation to the so-called "Kruskal rank" spark(A) − 1) or matrix completion [356]. When working in the binary field F 2 , the spark problem amounts to computing the minimum (Hamming) distance of a binary linear code, which-along with the strongly related problem of maximum-likelihood decoding-has been treated extensively in the coding theory community, see, e.g., the structural and polyhedral results and LP and MIP techniques discussed in [286,352,142,208,20,203,285] and references therein.…”