On binary sliding block codes

Sliding block codes are an intriguing alternative to the block codes used in the development of classical information theory. The fundamental analytical problem associated with the use of a sliding block code (SBC) for source encoding with respect to a fidelity criterion is that of determining the entropy of the coder output. Several methods of calculating and of bounding the output entropy of an SBC are presented. The local and global behaviors of a well-designed SBC also are discussed. The so-called "101-coder," which eliminates all the isolated zeros from a binary input, plays a central role. It not only provides a specific example for application of the techniques developed for calculating and bounding the output entropy, but also serves as a medium for obtaining indirect insight into the problem of characterizing a good SBC. An easily implementable SBC subclass is introduced in which the outputs can be calculated by simple logic circuitry. The study of this subclass is shown to be closely linked with the theory of algebraic group codes.