Technical Report CS0866

TR#:CS0866
Class:CS
Title: ON THE DECODING DELAY OF ENCODERS FOR INPUT-CONSTRAINED CHANNELS.
Authors: J.J. Ashley, B.H. Marcus and R.M. Roth
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Abstract: Finite-state encoders that encode $n$-ary data into a constrained system $S$ are considered. The anticipation, or decoding delay, of such an $(S,n)$-encoder is the number of symbols that a state-dependent decoder needs to look ahead in order to recover the current input symbol. Upper bounds are obtained on the smallest attainable number of states of any $(S,n)$-encoder with anticipation $t$. Those bounds can be explicitly computed from $t$ and $S$, which implies that the problem of checking whether there is an $(S,n)$-encoder with anticipation $t$ is decidable. It is also shown that if there is an $(S,n)$-encoder with anticipation $t$, then a version of the state-splitting algorithm can be applied to produce an $(S,n)$ encoder with anticipation at most $2t-1$. We also observe that the problem of checking whether there is an $(S,n)$-encoder having a sliding-block decoder with a given memory and anticipation is decidable.
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