Construction of encoders with small decoding look-ahead for input-constrained channels

Abstract

An input-constrained channel is defined as the set S of finite sequences generated by a finite labeled directed graph which defines the channel. A construction based on a result of Adler, Goodwyn, and Weiss (1977) is presented for finite-state encoders for input-constrained channels. Let G=(V, E) denote a smallest deterministic presentation of S. For a given input-constrained channel S and for any rate p: q up to the capacity c(S) of S, the construction provides finite-state encoders of fixed-rate p: q that can be implemented in hardware with a number of gates which is at most polynomially large in |V|. When p/q<c(S), the encoders have order /spl les/12|V|, namely, they can be decoded by looking ahead at up to 12|V| symbols, thus improving slightly on the order of previously known constructions. A stronger result holds when p/q/spl les/c(S)-((log/sub 2/, e)/(2/sup P/q)) and S is of finite memory, where the encoders can. Be decoded by a sliding-block decoder with look-ahead /spl les/2|V|+1.<<ETX>>