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 $\alpha$ in the random coding sense and in the TRC exponent sense are different from one another, and they are both different from the optimal $\alpha$ 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.
翻译:我们为随机状态的通信频道生成了各种错误提示, 仅在编码器中可以提供。 对于限量的alphabet Gel'fand- Pinsker 频道及其 Gausian 对应频道, 脏纸频道, 我们随机地生成了随机的代码提示, 典型随机代码( TRCs) 的错误提示, 以及清除代码的错误提示。 对于两个频道模型, 我们分析一些亚最佳的 bin- indarder 解码器, 这些解码器在功能下是尽可能最佳的, 至少对于随机的编码错误, 至少在随机的编码错误前显示。 对于脏纸频道, 我们通过一个数字示例示例显示, 真相与和解委员会的错误预示出, 以及 Expigation Expenter 严格地改进了随机的编码( TRC), 以相对较低的编码速度, 这是已知的, 对于没有随机的频道来说, 没有随机的 Bin- indker 频道, 最优值是它们最差的值值 $\\\ codeal a decol decol decreal cal decreal cal cadeal decreal decreal a lavelop ladeal decre ex decreal cal decreal decreal decreal decreal lautal decal lautal lautal lautal lautal excal decal decal acudecudeal 。