Asymptotic properties on codeword lengths of an optimal FV code for general sources
This correspondence is concerned with asymptotic properties on the codeword length of a fixed-to-variable length code (FV code) for a general source {X-n}(n = 1)(infinity) with a finite or countably infinite alphabet. Suppose that for each n >= 1 X-n is encoded to a binary codeword phi(n)(X-n) of length i(phi(n)(X-n)). Letting epsilon(n) denote the decoding error probability, we consider the following two criteria on FV codes: i) epsilon n = 0 for all n >= 1 and ii) lim sup(n ->infinity) epsilon(n)   0 in probability as n -> infinity under a certain condition, where P-Xn denotes the probability distribution of Xn. Under criterion ii), we first determine the minimum rate achieved by FV codes. Next, we show that 1/n l (phi(n)(Xn)) of an arbitrary FV code achieving the minimum rate in a certain sense has a property similar to the lossless case.
general source fixed-to-variable length coding asymptotic optimality convergence in distribution information spectrum