Efficient Computation and Optimization of the Free Distance of Variable-Length Finite-State Joint Source-Channel Codes

This paper considers the optimization of a class of joint source-channel codes described by finite-state encoders (FSEs) generating variable-length codes. It focuses on FSEs associated to joint source-channel integer arithmetic codes, which are uniquely decodable codes by design. An efficient method for computing the free distance of such codes using Dijkstra´s algorithm is proposed. To facilitate the search for codes with good distance properties, FSEs are organized within a tree structure, which allows the use of efficient branch-and-prune techniques avoiding a search of the whole tree.