A SAT-Based Scheme to Determine Optimal Fix-Free Codes

Fix-free or reversible-variable-length codes are prefix condition codes which can also be decoded in the reverse direction. They have attracted attention from several communities and are used in video standards. Two variations of fix-free codes (with additional constraints) have also been considered for joint source-channel coding: 1) "symmetric" fix-free codes, which require the codewords to be palindromes; 2) fix-free codes with distance constraints on pairs of codewords. We propose a new approach to determine the existence of a fix-free code with a given set of codeword lengths, for each of the three variations of the problem. We also describe a branch-and-bound algorithm to find the collection of optimal codes for asymmetric and symmetric fix-free codes.