A note on the Shannon capacity of run-length-limited codes (Corresp.)

It is proven that 100-percent efficient fixed-rate codes for run-length-limited (RLL)(d,k)and RLL charge-constrained(d, k; c)channels are possible in only two eases, namely(d,k; c)=(0,1;1)and(1,3;3). Specifically, the binary Shannon capacity of RLL(d, k)constrained systems is shown to be irrational for all values of(d, k),0 ≤ d < k. For RLL charge-constrained systems with parameters(d, k;c), the binary capacity is irrational for all values of(d, k; c),0 ≤ d < k,2c ≥ k + 1, except(0,1; 1)and(1,3;3), which both have binary capacity1/2.