Asymptotic Behavior and Typicality Properties of Runlength-Limited Sequences

This paper studies properties of binary runlength-limited sequences with additional constraints on their Hamming weight and/or number runs identical symbols. An algebraic and a probabilistic (entropic) characterization the exponential growth rate such sequences, i.e., information capacity, are obtained by using methods multivariate analytic combinatorics, capacity as function its parameters stated. The second-order term in asymptotic expansion these is also given, typical values relevant quantities derived. Several applications results illustrated, including bounds codes for weight-preserving run-preserving channels (e.g., insertion-deletion channel), sphere-packing bound sparse error patterns, asymptotics constant-weight sub-block constrained sequences. In addition, closely related notion— $q$ -ary fixed Manhattan weight—is briefly discussed, an application coding molecular timing illustrated.