NOTE ON THE SHANNON CAPACITY OF RUN-LENGTH-LIMITED CODES.

Abstract

The authors prove that 100% efficient fixed-rate codes for run-length-limited (RLL) (d,k) and RLL charge-constrained (d, k; c) channels are possible in only two cases, namely (d, k; c) equals (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 less than equivalent to d less than equivalent to k. For RLL charge-constrained systems with parameters (d, k; c), the binary capacity is irrational for all values of (d, k; c),0 less than equivalent to d less than equivalent to k, 2c greater than equivalent to k plus 1, except (0, 1; 1) and (1, 3; 3), which both have binary capacity 1/2.