Runlength codes from source codes

A class of binary runlength codes, also known as (d,k) codes, is analyzed. These codes are developed by constructing a lossless source code that maps runlengths into unconstrained binary sequences. The source code is constructed for the maxentropic distribution on runlengths. The inverse of the source code, which outputs runlengths guided toward the ideal maxentropic distribution, is the (d,k) code. Four types of source codes are investigated for this purpose: Huffman, enumerative, variable-length-to-block, and Elias or arithmetic. The rates of the codes are each proven to converge to the capacity with increasing complexity. The codes are not state dependent and are variable rate except for the fixed-rate enumerative code. A combined source-(d,k) code is presented that is based on the arithmetic code.