A Linear Bound for Sliding-Block Decoder Window Size

Abstract

Adler, Coppersmith, and Hassner have presented methods for coding arbitrary nary sequences into certain constrained systems of sequences, those with finite memory, defined by labeled directed graphs. An example is the runlength-limited system for the magnetic recording channel. Their codes have limited error propagation because the decoders are sliding block with a finite window length. We present upper bounds on the necessary length of the decoder window. The bounds are linear in the memory, anticipation, and number of states of the original constraint graph presenting the constrained system. © 1988 IEEE