Analysis on the codeword generating process of an arithmetic code and its application to source distribution transformer

在整个项目中，我们对一个算术码的码字生成过程得到了如下结果。2004-我们从理论上评估了平均意义上由算术编码器生成的码字中包含的冗余。此外，我们还开发了一种将信息源符号序列转换为具有给定目标分布的另一个序列的算法。该算法解决了算术编码中存在的两个实际问题：1)译码过程停止时。2)如何从转换后的序列精确地再现原始序列。2005-我们考虑了以随机间隔输出符号的信息源的编码/解码过程，并研究了算术编码器在单位时间内输出的码符号的数量，即码字的片段及其输出的间隔。计算机实验表明，碎片的间隔可以用几何分布来建模，而每个碎片的长度是不同的。我们在解码器侧观察到类似的结果。也就是说，算法解码器输出码字的片段，该码字在其区间上具有几何分布。然而，我们的实验表明，片段的长度既不是单个的，也不是几何分布的。最后，我们研究了编码过程的延迟，并评估了无记忆二进制源的延迟概率分布。

Throughout this project, we have obtained the following results on the codeword generating process of an arithmetic code.2004-We evaluated theoretically, in the average sense, the redundancy included in a codeword generated by an arithmetic encoder. Moreover, we developed an algorithm to transform a sequence of information source symbols into another sequence with a given target distribution. This algorithm dissolve the following two practical problems that result from arithmetic codes:1) when the decoding process halt.2) how to reproduce exactly the original sequence from the transformed one.2005-We considered the encoding/decoding processes for an information source that outputs symbols with a random interval and studied on the number of code symbols, that is, a fragment of a codeword, that an arithmetic encoder outputs at a unit time and the interval that it outputs them. From computer experiments, the interval of fragments can be modeled by geometric distribution while the length of each fragment has a different one. We observed the similar results in the decoder side. That is, the arithmetic decoder outputs a fragment of a codeword with a geometric distribution on its interval. However, our experiments showed that the length of fragment is neither individual nor geometrically distributed. Finally, we investigate the delay of the coding process and evaluated the probability distribution of the delay for a memoryless binary source.