论文标题
肮脏纸和凝胶式pinsker通道的错误指数
Error Exponents of the Dirty-Paper and Gel'fand-Pinsker Channels
论文作者
论文摘要
我们为具有随机状态的通信通道得出了各种错误指数，这些指数仅在编码器上可用。对于有限的alphabet gel'fand-pinsker通道及其高斯对应物（肮脏的纸通道），我们得出了随机编码指数，典型随机代码（TRC）的误差指数以及消除代码的错误指数。对于两个通道模型，我们分析了一些亚最佳的bin索引解码器，这些解码器至少对于随机编码误差指数，这些解码器在渐近上是最佳的。对于肮脏的纸通道，我们通过数值示例明确显示，以相对较低的编码率，TRC的误差指数和消除的指数严格改进了随机编码指数，这是无随机状态的离散无内存通道的已知事实。我们还表明，以低于容量的速率，在随机编码意义上，在TRC指数中，肮脏纸设计参数$α$的最佳值彼此不同，它们与达到通道容量所需的最佳$α$不同。对于Gel'Fand-Pinsker通道，我们允许进行可变的随机套件构建，并证明先前提议的最大惩罚互助信息解码器在给定的解码器类别中渐近最佳，至少对于随机编码误差指数。
We derive various error exponents for communication channels with random states, which are available non-causally at the encoder only. For both the finite-alphabet Gel'fand-Pinsker channel and its Gaussian counterpart, the dirty-paper channel, we derive random coding exponents, error exponents of the typical random codes (TRCs), and error exponents of expurgated codes. For the two channel models, we analyze some sub-optimal bin-index decoders, which turn out to be asymptotically optimal, at least for the random coding error exponent. For the dirty-paper channel, we show explicitly via a numerical example, that both the error exponent of the TRC and the expurgated exponent strictly improve upon the random coding exponent, at relatively low coding rates, which is a known fact for discrete memoryless channels without random states. We also show that at rates below capacity, the optimal values of the dirty-paper design parameter $α$ in the random coding sense and in the TRC exponent sense are different from one another, and they are both different from the optimal $α$ that is required for attaining the channel capacity. For the Gel'fand-Pinsker channel, we allow for a variable-rate random binning code construction, and prove that the previously proposed maximum penalized mutual information decoder is asymptotically optimal within a given class of decoders, at least for the random coding error exponent.
