论文标题
广义随机Gilbert-Varshamov代码：典型的误差指数和浓度属性
Generalized Random Gilbert-Varshamov Codes: Typical Error Exponent and Concentration Properties
论文作者
论文摘要
我们发现恒定组成的确切典型误差指数在DMCS通道上具有通用的可能性解码的DMCS通道上的代码。我们表明，RGV集合的典型误差指数等于所消除的错误指数，前提是适当地选择RGV代码书参数。我们还证明，随机编码指数以概率收敛到典型的误差指数，并得出了相应的非肌浓度率。我们的结果表明，下尾的衰减速率是指数级的，而上尾的衰减速率在消耗的误差指数上方是双重指数。表征了衰减速率对RGV距离功能的明确依赖性。
We find the exact typical error exponent of constant composition generalized random Gilbert-Varshamov (RGV) codes over DMCs channels with generalized likelihood decoding. We show that the typical error exponent of the RGV ensemble is equal to the expurgated error exponent, provided that the RGV codebook parameters are chosen appropriately. We also prove that the random coding exponent converges in probability to the typical error exponent, and the corresponding non-asymptotic concentration rates are derived. Our results show that the decay rate of the lower tail is exponential while that of the upper tail is double exponential above the expurgated error exponent. The explicit dependence of the decay rates on the RGV distance functions is characterized.
