This paper addresses the design of joint source-channel variable-length codes with maximal free distance for given codeword lengths. While previous design methods are mainly based on bounds on the free distance of the code, the proposed algorithm exploits an exact characterization of the free distance. The code optimization is cast in the framework of mixed-integer linear programming and allows to tackle practical alphabet sizes in reasonable computing time.

This paper proposes branch-and-prune algorithms for searching prefix-free joint source-channel codebooks with maximal free distance for given codeword lengths. For that purpose, it introduces improved techniques to bound the free distance of variable-length 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.

This paper considers the optimization of Error-Correcting Variable-Length Codes (EC-VLC), which are a class of joint-source channel codes. The aim is to find a prefix-free codebook with the largest possible free distance for a given set of codeword lengths, ℓ = (ℓ1, ℓ2, ..., ℓM). The proposed approach consists in ordering all possible codebooks associated to ℓ on a tree, and then to apply an efficient branch-and-prune algorithm to find a codebook with maximal free distance. Three methods for building the tree of codebooks are presented and their efficiency is compared.