Tamir Averbuch Ran, Merhav Neri
The Andrew and Erna Viterbi Faculty of Electrical Engineering, Technion - Israel Institute of Technology, Technion City, Haifa 3200003, Israel.
Entropy (Basel). 2021 Feb 24;23(3):265. doi: 10.3390/e23030265.
Typical random codes (TRCs) in a communication scenario of source coding with side information in 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 TRCs 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 exponential vanish when the blocklength tends to infinity.
解码器中具有边信息的信源编码通信场景下的典型随机码（TRC）是本工作的主要研究对象。我们研究半确定性码集合，它是普通随机分箱码集合的一种特定变体。在这个码集合中，源的相对较小的类型类以一对一的方式确定性地划分到可用的箱中。因此，错误概率会大幅降低。推导了随机分箱错误指数和TRC的错误指数，并证明在一些重要的特殊情况下它们彼此相等。我们表明，某些通用解码器，例如具有经验熵度量的随机似然解码器，也可以实现最优解码下的性能。此外，我们讨论了典型随机半确定性码的错误指数和超额速率指数之间的权衡，并刻画了其最优速率函数。我们表明，对于任何一对相关信息源，当码长趋于无穷大时，错误概率和超额速率概率都会指数级消失。
