Joint Coding for Discrete Sources and Finite-State Noiseless Channels

We propose a joint coding scheme using multiple code tables to efficiently transmit a sequence of messages of a discrete memoryless source (DMS) through a finite-state noiseless channel with unequal costs of code letters, which includes a noiseless (d, k)-constrained channel as a particular case. This paper presents a methodology for code design based on two methods. The first method, integer programming, is used to optimize a prefix-free code at each channel state when codeword costs are unequal and vary with each state. The second method is an iterative optimization that minimizes the average cost of the joint coding scheme using multiple code tables. The proposed coding scheme achieves the optimal average cost in the class of joint coding schemes using multiple code tables of prefix-free codes for a given pair of DMS and finite-state channel.