On the decoding delay of encoders for input-constrained channels

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.