非对称数制
Asymmetric numeral systems
摘要：
本文将提出新的方法熵编码：家庭的推广标准的数字系统是最佳的编码序列的等概率符号，到非对称数字系统-最佳的自由选择的概率分布的符号。它与范围编码有一些相似之处，但不是在选择范围时对符号进行编码，而是将这些范围均匀地分布在整个区间上。这导致更简单的编码器-而不是使用两个状态来定义范围，我们只需要一个。这种方法是非常普遍的-我们可以获得从非常精确的编码（ABS）到非常快的可能性，以额外加密数据（ANS）。该加密方法使用密钥初始化随机数生成器，用于计算编码表。这种预先初始化的加密还有一个额外的优点：可以抵抗蛮干攻击--为了检查密钥，我们必须进行整个初始化。还将提出新的纠错方法的应用：在每一步中出现错误后，我们选择概率来观察错误。还将提出新的纠错方法的应用：在每一步中出现错误后，我们选择概率来观察错误。对于任何噪声水平，我们都可以通过这种方式接近香农极限，并且预期线性校正时间。
英文摘要：
In this paper will be presented new approach to entropy coding: family of generalizations of standard numeral systems which are optimal for encoding sequence of equiprobable symbols, into asymmetric numeral systems - optimal for freely chosen probability distributions of symbols. It has some similarities to Range Coding but instead of encoding symbol in choosing a range, we spread these ranges uniformly over the whole interval. This leads to simpler encoder - instead of using two states to define range, we need only one. This approach is very universal - we can obtain from extremely precise encoding (ABS) to extremely fast with possibility to additionally encrypt the data (ANS). This encryption uses the key to initialize random number generator, which is used to calculate the coding tables. Such preinitialized encryption has additional advantage: is resistant to brute force attack - to check a key we have to make whole initialization. There will be also presented application for new approach to error correction: after an error in each step we have chosen probability to observe that something was wrong. There will be also presented application for new approach to error correction: after an error in each step we have chosen probability to observe that something was wrong. We can get near Shannon's limit for any noise level this way with expected linear time of correction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
