广义自适应码编码的特殊情况
Special Cases of Encodings by Generalized Adaptive Codes
摘要：
自适应（可变长度）码根据输入数据串中的先前符号将可变长度码字与正被编码的符号相关联。此类代码已在[Dragos Trinca，cs.DS/0505007]中作为一类新的非标准变长代码提出。广义自适应码（简称GA码）也在[Dragos Trinca，cs.DS/0505007]中提出，不仅作为一类新的非标准变长码，而且作为任意阶自适应码的自然推广。本文的目的是继续发展理论的变长码建立几个有趣的自适应码和其他类别的代码之间的联系。不仅从理论的角度（通过证明新的结果），但也从一个应用（通过提出几个应用）的连接进行了讨论。首先，我们证明了自适应霍夫曼编码和Lempel-Ziv编码是GA码编码的特殊情况。其次，我们证明了任何满足一定条件的（n，1，m）卷积码都可以建模为m阶自适应码。第三，我们描述了一个基于自适应码和卷积码之间的联系的密码方案，并提出了一个有见地的分析这个方案。最后，我们总结推广自适应码（p，q）-自适应码，并讨论自适应码和时变码之间的联系。
英文摘要：
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 [Dragos Trinca, cs.DS/0505007] as a new class of non-standard variable-length codes. Generalized adaptive codes (GA codes, for short) have been also presented in [Dragos Trinca, cs.DS/0505007] not only as a new class of non-standard 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 order m. 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.
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