An entropy theorem for computing the capacity of weakly (d,k)-constrained sequences

We find an analytic expression for the maximum of the normalized entropy -/spl Sigma//sub i/spl epsiv/T/p/sub i/ln p/sub i///spl Sigma//sub i/spl epsiv/T/ip/sub i/ where the set T is the disjoint union of sets S/sub n/ of positive integers that are assigned probabilities P/sub n/, /spl Sigma//sub n/P/sub n/=1. This result is applied to the computation of the capacity of weakly (d,k)-constrained sequences that are allowed to violate the (d,k)-constraint with small probability.