Optimal Parsing Trees for Run-Length Coding of Biased Data

We study coding schemes which encode unconstrained sequences into run-length-limited (d, k)-constrained sequences. We present a general framework for the construction of such (d, k)-codes from variable-length source codes. This framework is an extension of the previously suggested bit stuffing, bit flipping, and symbol sliding algorithms. We show that it gives rise to new code constructions which achieve improved performance over the three aforementioned algorithms. Therefore, we are interested in finding optimal codes under this framework, optimal in the sense of maximal achievable asymptotic rates. However, this appears to be a difficult problem. In an attempt to solve it, we are led to consider the encoding of unconstrained sequences of independent but biased (as opposed to equiprobable) bits. Here, our main result is that one can use the Tunstall source coding algorithm to generate optimal codes for a partial class of (d, k) constraints.