A linear bound for sliding-block decoder window size. II

Abstract

For pt.I see ibid., vol.34, p. 389-99, 1988. An input-constrained channel is the set S of finite sequences of symbols generated by the walks on a labeled finite directed graph G (which is said to present S). We introduce a new construction of finite-state encoders for input-constrained channels. The construction is a hybrid of the state-splitting technique of Adler, Coppersmith, and Hassner (1983) and the stethering technique of Ashley, Marcus, and Roth (see ibid., vol.41, p.55-76, 1995). When S has finite memory, and p and g are integers where p/g is at most the capacity of S, the construction guarantees an encoder at rate p:g and having a sliding-block decoder (literally at rate q:p) with look-ahead that is linear in the number of states of the smallest graph G presenting S. This contrasts with previous constructions. The straight Adler, Coppersmith, and Hassner construction provides an encoder having a sliding-block decoder at rate q:p, but the best proven upper bound on the decoder look-ahead is exponential in the number of states of G. A previous construction of Ashley provides an encoder having a sliding-block decoder whose look-ahead has been proven to be linear in the number of states of G, but the decoding is at rate tq:tp, where t is linear in the number of states of G.