Research on source coding theorems for a multi-terminal communication system with a two-way channel

本文研究了具有双向信道的多终端通信系统的信源编码问题，该系统是著名的Slepian-Wolf系统的扩展系统。在Slepian-Wolf系统中，相关的源输出X和Y由两个单独的编码器fx和fy独立地编码，并且解码器g在任意小的错误概率内再现X和Y。扩展系统由两个编码器fx和fy以及两个解码器gx和戈伊组成，这两个编码器fx和fy以与Slepian-Wolf系统相同的方式分别对X和Y进行编码。编码器和解码器通过信道fx*gx、fi* 戈伊、gx戈伊连接<tautomer>。两个解码器通过双向通道连接，在gx和戈伊分别再现X和Y之前，它们相互通信。信源编码问题是确定一个可达速率域，使得当且仅当三个信道的四种速率都包含在可达速率域中时，可以获得任意小的译码错误概率。(1)它示出的处理系统的可实现的区域不能来自各种多终端系统的已知结果，它是澄清为什么编码问题变得困难，如果一个双向信道包括在通信系统中。(2)从理论上推导了可实现区域的外速率区域和内速率区域。(3)以下问题也在信源编码的范围内被研究，尽管它们与上述问题没有直接关系。(a)（B）灰度图象的命中树加权法，（c）分块排序数据压缩算法的理论分析，（d）新的正整数递归泛码。

This research treats a source coding problem for a multi-terminal communication system with a two-way channel, which is an extended system of the well-known Slepian-Wolf system. In the Slepian-Wolf system, correlated source outputs X and Y are encoded by two separate encoders, fx and fy, independently, and decoder g reproduces X and Y within an arbitrarily small error probability.The extended system consists of two encoders fx and fy, which encode X and Y, respectively, in the same way as the Slepian-Wolf system, and two decoders gx and gy. The encoders and decoders are connected by channels as fx*gx, fi*gy, gx <tautomer> gy. Two decoders are connected by a two-way channel, and they communicate each other before gx and gy reproduce X and Y respectively. The source coding problem is to determine the achievable rate region such that arbitrarily small decoding error probability can be attained if and only if the four rates of three channels are included in the achievable rate region.The main results of this research is the following.(1) It is shown that the achievable region of the treated system cannot be derived from the known results for various multi-terminal systems, and it is clarified why the coding problem becomes difficult if a two-way channel is included in the communication system.(2) Outer and inner rate regions for the achievable region are derived theoretically.(3) The following problems have also been studied in the scope of source coding although they are not directly related to the above problem. (a) Analysis on the redundancy for universal codes with distortion, (b) Hit tree weighting method for gray scaled images, (c) Theoretical analysis on block sort data compression algorithm, (d) New recursive universal codes of the positive integers.