Interval algorithm for homophonic coding

It is shown that the idea of the successive refinement of interval partitions, which plays the key role in the interval algorithm for random number generation proposed by Han and Hoshi (see ibid., vol.43, p.599-611, 1997) is also applicable to the homophonic coding. An interval algorithm for homophonic coding is introduced which produces an independent and identically distributed (i.i.d.) sequence with probability p. Lower and upper bounds for the expected codeword length are given. Based on this, an interval algorithm for fixed-to-variable homophonic coding is established. The expected codeword length per source letter converges to H(X)/H(p) in probability as the block length tends to infinity, where H(X) is the entropy rate of the source X. The algorithm is asymptotically optimal. An algorithm for fixed-to-fixed homophonic coding is also established. The decoding error probability tends to zero as the block length tends to infinity. Homophonic coding with cost is generally considered. The expected cost of the codeword per source letter converges to c~H(X)/H(p) in probability as the block length tends to infinity, where, c~ denotes the average cost of a source letter. The main contribution of this paper can be regarded as a novel application of Elias' coding technique to homophonic coding. Intrinsic relations among these algorithms, the interval algorithm for random number generation and the arithmetic code are also discussed.