Decoding Binary Linear Block Codes Using Local Search

This paper presents a novel iterative hard decision decoding algorithm for binary linear block codes over a binary symmetric channel (BSC). The problem is formulated as a 0-1 integer programming problem which is known to be NP-hard. When the crossover probability c of the channel is known, the solution space of the decoding problem can be decreased to a sphere whose radius is related to c. Using the penalty function method, the problem is reformulated on this reduced solution space. Then an iterative multi-flip local search algorithm is designed to find the global solution of this decoding problem. For a code with minimum distance d, when the radius of the sphere is not greater than d-1/2, this algorithm has the maximum likelihood (ML) certificate property, i.e., if the decoder outputs a codeword, it is guaranteed to be the ML codeword. Compared to the probabilistic suboptimal iterative belief propagation (BP) decoder, this approach has lower complexity and better performance. Numerical results show that in terms of speed and performance the proposed decoding method outperforms BP decoding in the error floor region.