An efficient universal coding algorithm for noiseless channel with symbols of unequal cost

This paper describes an effcient and simple coding algorithm of universally optimal codes for stationary (ergodic) sources and noiseless channel with unequal symbol costs. The symbol cost indicates the required time (or space) for the transmission (or storage) of that symbol, and the cost of any code symbol depends only on that symbol. The proposed coding algorithm mainly consists of two parts. The first part is based on the well-known Ziv-Lempel coding algorithm proposed in 1978 (sometimes called LZ78), and the second part is based on the Varn coding algorithm. The coding algorithm asymptotically achieves an optimal average cost of codes for stationary sources, and also achieves an optimal cost of codes for stationary ergodic sources with probability one. Furthermore, the computational complexity of the proposed coding algorithm is linear with respect to the length of source sequence and coded sequence.