On the capacity of the (d, k) constrained BSC: computed bounds and estimates

The author computes upper and lower bounds on the capacity of the binary symmetric channel with a run-length constrained input. The upper bound is taken from some recent work. the lower bound is a new result based upon the idea that the capacity of a binary symmetric channel combined with a specific run-length limited block code is no larger than the capacity of the constrained binary symmetric channel. The bounds, denoted I_n^U and I_n ^L for the upper bound and the lower bound, respectively, are functions of an integer parameter n, with the bounds generally being tighter for larger n. The bounds are computed for n up to 8. Results are given as a function of the binary symmetry channel error probability, p. Using the bounds, the author computes estimates of capacity as well, using a technique described previously. Also included are computed bounds on the capacity of the binary symmetric channel combined with specific run-length limited codes, including the Miller code, a (2, 7) sliding block code, the (1, 7) Jacoby code, and some distance preserving run-length limited codes