Variable-to-Fixed Length Homophonic Coding with a Modified Shannon-Fano-Elias Code

Homophonic coding is a framework to reversibly convert a message into a sequence with some target distribution. This is a promising tool to generate a codeword with a biased code-symbol distribution, which is required for capacity-achieving communication by asymmetric channels. It is known that asymptotically optimal homophonic coding can be realized by a Fixed-to-Variable (FV) length code using an interval algorithm similar to a random number generator. However, FV codes are not preferable as a component of channel codes since a decoding error propagates to all subsequent codewords. As a solution for this problem an asymptotically optimal Variable-to-Fixed (VF) length homophonic code, dual Shannon-Fano-Elias-Gray (dual SFEG) code, is proposed in this paper. This code can be interpreted as a dual of a modified Shannon-Fano-Elias (SFE) code based on Gray code. It is also shown as a by-product that the modified SFE code, named SFEG code, achieves a better coding rate than the original SFE code in lossless source coding.