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Polynomial Asymptotically Optimal Coding of Underdetermined Bernoulli Sources of the General Form
Problems of Information Transmission ( IF 1.2 ) Pub Date : 2021-01-27 , DOI: 10.1134/s0032946020040079
L. A. Sholomov

An underdetermined Bernoulli source generates symbols of a given underdetermined alphabet independently with some probabilities. To each underdetermined symbol there corresponds a set of basic (fully defined) symbols such that it can be substituted (specified) by any of them. An underdetermined source is characterized by its entropy, which is implicitly introduced as a minimum of a certain function and plays a role similar to the Shannon entropy for fully defined sources. Coding of an underdetermined source must ensure, for any sequence generated by the source, recovering some its specification. Coding is asymptotically optimal if the average code length is asymptotically equal to the source entropy. Coding is universal if it does not depend on the probabilities of source symbols. We describe an asymptotically optimal universal coding method for underdetermined Bernoulli sources for which the encoding and decoding procedures can be realized by RAM-programs of almost linear complexity.



中文翻译:

一般形式的不确定Bernoulli源的多项式渐近最优编码

一个不确定的伯努利源独立地生成给定的不确定字母的符号,并且具有一些概率。每个未确定的符号都有一组基本的(完全定义的)符号,以便可以用它们中的任何一个代替(指定)。不确定源的特征在于其熵,它的隐含性是某些函数的最小值,它的作用类似于完全定义源的Shannon熵。对于源产生的任何序列,未确定源的编码必须确保恢复其某些规范。如果平均代码长度渐近等于源熵,则编码是渐近最优的。如果编码不取决于源符号的概率,则编码是通用的。

更新日期:2021-01-28
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