Technical Report CS0965

Title: Lower bounds on the anticipation of encoders for input-constrained channels
Authors: Gitit Ruckenstein and Ron M. Roth
Abstract: An input-constrained channel S is defined as the set of words generated by a finite labeled directed graph. A fixed-rate finite-state encoder for S is a finite-state machine E that maps unconstrained binary sequences into sequences of S in a lossless manner, and the anticipation of E measures the smallest decoding look-ahead of any decoder of E. It is shown that every fixed-rate finite-state encoder with finite anticipation for S can be obtained through state-spitting rounds applied to a certain graph presentation of S. By further characterizing the properties of such state-splitting rounds, lower bounds are derived on the anticipation of any fixed-rate finite state encoder for S with a given rate p:q. Those lower bounds improve on previously known bounds and, in particular, they are shown to be tight for the common rates used for the (1,7)-RLL and (2,7)-RLL constraints.
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