典型睡狼码的误差和超额率指数的权衡

Ran Averbuch, N. Merhav
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摘要

本文的主要研究对象是具有侧信息的源编码通信场景中的典型随机码(TRC)。研究了半确定性码集,它是普通随机分组码集的一种变体。在这个代码集成中,源的相对较小的类型类以一对一的方式确定地划分到可用的箱子中。因此,错误概率显著降低。推导了随机分组误差指数和随机分组误差指数,并在几个重要的特殊情况下证明了它们是相等的。我们证明了某些通用解码器也可以达到最优解码的性能,例如具有经验熵度量的随机似然解码器。此外,我们讨论了典型随机半确定性码的误差指数和超额率指数之间的权衡,并描述了其最优率函数。我们证明了对于任何一对相关信息源,误差和超额率概率都是指数消失的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Trade-Offs Between Error and Excess-Rate Exponents of Typical Slepian-Wolf Codes
Typical random codes (TRC) in a communication scenario of source coding with side information at the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random binning code ensemble. In this code ensemble, the relatively small type classes of the source are deterministically partitioned into the available bins in a one-to-one manner. As a consequence, the error probability decreases dramatically. The random binning error exponent and the error exponent of the TRC are derived and proved to be equal to one another in a few important special cases. We show that the performance under optimal decoding can be attained also by certain universal decoders, e.g., the stochastic likelihood decoder with an empirical entropy metric. Moreover, we discuss the trade-offs between the error exponent and the excess-rate exponent for the typical random semi-deterministic code and characterize its optimal rate function. We show that for any pair of correlated information sources, both error and excess-rate probabilities are exponentially vanishing.
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