有记忆擦除通道的首次通过时间和大偏差分析
First-Passage Time and Large-Deviation Analysis for Erasure Channels with Memory
摘要：
本文考虑了在有限状态擦除信道上传输信息的数字通信系统的性能。使用纠错码保护信息比特不受信道擦除的影响;码字的成功接收通过瞬时反馈在源处被确认。本研究的主要重点是延迟敏感的应用程序，代码与有限块长度，并必然，非零的解码失败的概率。这篇文章的贡献是双重的。介绍了一种计算清空缓冲区所需时间分布的方法。基于此分布，可以显式地计算到达空队列的平均命中时间和特定阈值的延迟违规概率。所提出的技术适用于传输缓冲器在数据传输开始时包含预定数量的信息比特的情况。此外，作为额外的性能标准，大偏差原则获得的经验平均服务时间和与通信过程相关的平均数据包传输时间。这个严格的框架产生一个务实的方法来选择码率和块长度的通信单元的服务要求的函数。实际系统的动机的例子，以进一步说明这些技术的适用性。
英文摘要：
This article considers the performance of digital communication systems transmitting messages over finite-state erasure channels with memory. Information bits are protected from channel erasures using error-correcting codes; successful receptions of codewords are acknowledged at the source through instantaneous feedback. The primary focus of this research is on delay-sensitive applications, codes with finite block lengths and, necessarily, non-vanishing probabilities of decoding failure. The contribution of this article is twofold. A methodology to compute the distribution of the time required to empty a buffer is introduced. Based on this distribution, the mean hitting time to an empty queue and delay-violation probabilities for specific thresholds can be computed explicitly. The proposed techniques apply to situations where the transmit buffer contains a predetermined number of information bits at the onset of the data transfer. Furthermore, as additional performance criteria, large deviation principles are obtained for the empirical mean service time and the average packet-transmission time associated with the communication process. This rigorous framework yields a pragmatic methodology to select code rate and block length for the communication unit as functions of the service requirements. Examples motivated by practical systems are provided to further illustrate the applicability of these techniques.
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