Special Cases of Encodings by Generalized Adaptive Codes

Adaptive (variable-length) codes associate variable-length codewords to symbols being encoded depending on the previous symbols in the input data string. This class of codes has been presented in [10, 11] as a new class of non-standard variable-length codes. Generalized adaptive codes (GA codes, for short) have been also presented in [10, 11] not only as a new class of nonstandard variable-length codes, but also as a natural generalization of adaptive codes of any order. This paper is intended to continue developing the theory of variable-length codes by establishing several interesting connections between adaptive codes and other classes of codes. The connections are discussed not only from a theoretical point of view (by proving new results), but also from an applicative one (by proposing several applications). First, we prove that adaptive Huffman encodings and Lempel-Ziv encodings are particular cases of encodings by GA codes. Second, we show that any (n; 1;m) convolutional code satisfying certain conditions can be modelled as an adaptive code of orderm. Third, we describe a cryptographic scheme based on the connection between adaptive codes and convolutional codes, and present an insightful analysis of this scheme. Finally, we conclude by generalizing adaptive codes to (p; q)-adaptive codes, and discussing connections between adaptive codes and time-varying codes.