Variable-length codes for channels with memory and feedback: Error-exponent lower bounds
Variable-length codes for channels with memory and feedback: Error-exponent lower bounds
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带内存和反馈的通道的可变长度代码：误差指数下限
DOI：
10.1109/isit.2017.8006778
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Jui Wu
中科院分区：
文献类型：
--
作者：
A. Anastasopoulos;Jui Wu
在伯纳舍夫（Burnashev）的经典著作中，发现了具有无噪声反馈和变长编码的无记忆信道的可靠度函数是平均速率的线性函数。在本文中，我们考虑了具有无噪声反馈的单一信道，并研究了特定的传输方案，其性能为信道可靠性函数提供了下界。在类似的信道中，信道状态基于先前的状态、输入和输出以一种确定性的方式演变，并且发射器知道它，但接收器不知道它。我们考虑一个两级传输方案。在第一阶段，发送方和接收方将它们的共同信息汇总到一个M维向量中，该向量的元素位于相同信道的状态空间和一个M维概率质量函数中，M为消息数。当其中一个消息足够可靠时，进入第二阶段，解决二元假设检验问题。该分析假设发送方和接收方都存在一些共同的随机性，并基于对发送信息后验信念的对数似然比的研究，特别是对其多步漂移的研究。仿真结果证实了该边界与同行论文中推导的上界相比是紧密的。
The reliability function of memoryless channels with noiseless feedback and variable-length coding has been found to be a linear function of the average rate in the classic work of Burnashev. In this work we consider unifilar channels with noiseless feedback and study specific transmission schemes, the performance of which provides lower bounds for the channel reliability function. In unifilar channels the channel state evolves in a deterministic fashion based on the previous state, input, and output, and is known to the transmitter but is unknown to the receiver. We consider a two-stage transmission scheme. In the first stage, both transmitter and receiver summarize their common information in an M-dimensional vector with elements in the state space of the unifilar channel and an M-dimensional probability mass function, with M being the number of messages. The second stage, which is entered when one of the messages is sufficiently reliable, is resolving a binary hypothesis testing problem. The analysis assumes the presence of some common randomness shared by the transmitter and receiver, and is based on the study of the log-likelihood ratio of the transmitted message posterior belief, and in particular on the study of its multistep drift. Simulation results confirm that the bounds are tight compared to the upper bounds derived in a companion paper.