Exact asymptotics for the random coding error probability
Exact asymptotics for the random coding error probability
复制标题
随机编码错误概率的精确渐近
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
J. Honda
中科院分区：
文献类型：
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作者：
J. Honda
本文研究了无记忆信道中随机码的误码率。在通信系统中，允许的差错概率是很小的，讨论可达差错概率与其上界之间的相对差距有时比讨论绝对差距更重要。Scarlett等人利用鞍点逼近技术得到了随机编码联合界的一个很好的上界，但没有证明其上界的相对间隔收敛于零。本文推导出了一类无记忆信道的可达错误概率的新界。导出的界限是严格小于由斯嘉丽等人。和它的相对差距与随机编码错误概率（不是一个工会界）为固定的编码速率块长度的增加消失。
Error probabilities of random codes for memoryless channels are considered in this paper. In the area of communication systems, admissible error probability is very small and it is sometimes more important to discuss the relative gap between the achievable error probability and its bound than to discuss the absolute gap. Scarlett et al. derived a good upper bound of a random coding union bound based on the technique of saddlepoint approximation but it is not proved that the relative gap of their bound converges to zero. This paper derives a new bound on the achievable error probability in this viewpoint for a class of memoryless channels. The derived bound is strictly smaller than that by Scarlett et al. and its relative gap with the random coding error probability (not a union bound) vanishes as the block length increases for a fixed coding rate.