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

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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 .

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IEEE Transactions on Information Theory  (Volume:33 ,  Issue: 4 )