The theory of large deviations for Gibbs random fields is used to show that the asymptotic number of bits per symbol for Ziv-Lempel codes in two dimensions is given by the maximal entropy of all Gibbs fields with the same interaction. The error-probability is shown to converge exponentially fast to zero. In addition, the stronger version of the Shannon-McMillan theorem proved by D.S. Ornstein and B. Weiss (1990) is formulated and proved in terms of the exponential decay of the probability of the nontypical sequences. >
['Yali Amit', 'Michael I. Miller']
Large deviations for the asymptotics of Ziv-Lempel codes for 2-D Gibbs fields