On variable-to-fixed length coding of a general source with infinite alphabet

A converse coding theorem for a variable-to-fixed length (VF) source code is proved for a general source with count-ably infinite alphabet. In this result, redundancy is defined by the difference of the symbolwise codeword length and the symbolwise ideal codeword length. It is proved that the redundancy is nonnegative in probability for the codes such that the decoding error probability vanishes and the minimum message length becomes large. Moreover, the theorem is applied to the Tunstall code for finite-alphabet stationary and memoryless sources.