On a Conjecture on Error Recovery for Variable Length Codes

Maxted et al. in 1985 gave a conjecture stating that, for a Geometric source, the stable code has the best error recovery performance for the case of bit inversion among all Huffman codes for this source, while the unstable code has the worst error recovery performance. This conjecture was extended by Swaszek et al. ten years later, but without proof, to sources with certain probability mass function. In this paper, we prove the correctness of the extended version of this conjecture. Our proof provides a novel mathematical technique for proving the optimality of variable length code in the sense of error recovery capability. Furthermore, our result offers some insight into the working mechanism of the suffix condition that has been widely used by many heuristic algorithms to find error-resilient codes.