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 \leq 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 \leq d < k,2c \geq k + 1
, except
(0,1; 1)
and
(1,3;3)
, which both have binary capacity
1/2
.