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On the decoding delay of encoders for input-constrained channels

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3 Author(s)
J. J. Ashley ; IBM Res. Div., Almaden Res. Center, San Jose, CA, USA ; B. H. Marcus ; R. M. Roth

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

Published in:

IEEE Transactions on Information Theory  (Volume:42 ,  Issue: 6 )