# SLIDING-BLOCK CODING FOR INPUT-RESTRICTED CHANNELS.

## Abstract

Summary form only given. Coding arbitrary sequences into a constrained system of sequences (called a sofic system) is considered. Such systems model the input constraints for input-restricted channels (e. g. , run-length limits and spectral constraints for the magnetic recording channel). In this context, it is important that the code be noncatastrophic; for then the decoder will have limited error propagation. A constructive proof is given of the existence of finite-state, invertible, noncatastrophic codes from arbitrary n-ary sequences to a sofic system S at constant rate p:q provided only that Shannon's condition, (p/q) less than equivalent to (C/log n), is satisfied (C is the capacity of the system S). If strict inequality holds, or if equality holds and S satisfies a certain natural condition. A stronger result is obtained, namely, the decoders can be made state-independent sliding block.