On Source Coding with Coded Side Information for a Binary Source with Binary Side Information
On Source Coding with Coded Side Information for a Binary Source with Binary Side Information
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关于带有二进制辅助信息的二进制源的带有编码辅助信息的源编码
DOI：
10.1109/isit.2007.4557427
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
T. Ho
中科院分区：
文献类型：
--
作者：
Wei;R. Koetter;M. Effros;T. Ho
编码的边信息问题的无损速率区域被“解决”，但其解是用辅助随机变量来表示的。因此，要找到任何固定例子的速率区域，都需要对一族允许的辅助随机变量进行优化。虽然直观的构造很容易得到，并且在某些特殊条件下最优解是已知的，但即使对于像具有二进制边信息的二进制源这样的基本例子来说，证明最优解也是令人惊讶的困难。对于源信息和边信息都是二值的一类问题，我们得到了最优辅助随机变量和相应的可达速率域。我们的解决方案包括首先收紧辅助随机变量的字母表大小的已知界限，然后在该约束下优化辅助随机变量。用来收紧字母表大小界限的技术适用于各种问题，而不是这里研究的问题。
The lossless rate region for the coded side information problem is "solved" but its solution is expressed in terms of an auxiliary random variable. As a result, finding the rate region for any fixed example requires an optimization over a family of allowed auxiliary random variables. While intuitive constructions are easy to come by and optimal solutions are known under some special conditions, proving the optimal solution is surprisingly difficult even for examples as basic as a binary source with binary side information. We derive the optimal auxiliary random variables and corresponding achievable rate regions for a family of problems where both the source and side information are binary. Our solution involves first tightening known bounds on the alphabet size of the auxiliary random variable and then optimizing the auxiliary random variable subject to this constraint. The technique used to tighten the bound on the alphabet size applies to a variety of problems beyond the one studied here.