On the Loss of Single-Letter Characterization: The Dirty Multiple Access Channel
On the Loss of Single-Letter Characterization: The Dirty Multiple Access Channel
复制标题
关于单字母特征的丢失：脏多址信道
DOI：
10.1109/tit.2009.2018174
复制
发表时间：
2009
影响因子：
2.5
通讯作者：
R. Zamir
中科院分区：
文献类型：
--
作者：
T. Philosof;R. Zamir
对于一般的无内存系统，现有的信息理论解决方案具有ldquomingle-letterrdquo形式。这反映了以下事实：最佳性能可以通过随机代码（或随机封装方案）来处理，该代码使用某些标量分布的独立且相同分布的副本生成。这是任何（信息理论）问题的解决方案的形式吗？实际上，一些反词是已知的。最著名的是ldquotwo帮助Onerdquo问题：Korner和Marton表明，如果我们想从独立编码中解码两个相关二进制源的模量，则线性编码要比随机编码更好。在本文中，我们提供了另一个反示例，即ldquodoubly-dirtyrdquo多访问通道（MAC）。像Korner-Marton问题一样，这是一个多性场景，其中侧面信息分布在几个终端之间。每个发射器都知道通道干扰的一部分，而接收器仅观察通道输出。我们为二进制双重降低MAC的容量区域提供了明确的解决方案，证明了如何使用线性编码方案来接近该区域，并证明其中严格包含了Ldquobest已知的单个字母区域。我们还指出了关于高斯病例中单个字母表征的容量损失的猜想。
For general memoryless systems, the existing information-theoretic solutions have a ldquosingle-letterrdquo form. This reflects the fact that optimum performance can be approached by a random code (or a random binning scheme), generated using independent and identically distributed copies of some scalar distribution. Is that the form of the solution of any (information-theoretic) problem? In fact, some counter examples are known. The most famous one is the ldquotwo help onerdquo problem: Korner and Marton showed that if we want to decode the modulo-two sum of two correlated binary sources from their independent encodings, then linear coding is better than random coding. In this paper we provide another counter example, the ldquodoubly-dirtyrdquo multiple-access channel (MAC). Like the Korner-Marton problem, this is a multiterminal scenario where side information is distributed among several terminals; each transmitter knows part of the channel interference while the receiver only observes the channel output. We give an explicit solution for the capacity region of the binary doubly-dirty MAC, demonstrate how this region can be approached using a linear coding scheme, and prove that the ldquobest known single-letter regionrdquo is strictly contained in it. We also state a conjecture regarding the capacity loss of single-letter characterization in the Gaussian case.