Asymptotic properties of algorithms of data compression with fidelity criterion based on string matching

A data compression scheme proposed by Steinberg and Gutman [1993] is essentially an extension of the Ziv-Lempel algorithm [1977]. Their scheme, however, does not achieve the rate-distortion bound in their original form. In the present paper, sufficient conditions that the rate of the scheme achieves the rate-distortion bound are analyzed for discrete memoryless sources and memoryless gaussian sources under the single-letter fidelity criterion and squared-error fidelity criterion, respectively