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

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