CIF: Small: Channels with Memory -- Universal-Compression-Based Modeling Principles for Computing and Optimizing Information Rates

大多数物理通信信道的行为取决于信道过去的使用情况--也就是说，许多物理通信信道表现出“记忆”。接下来的挑战是构建能够最佳利用通道记忆的工具。此外，通常的信息理论分析方法甚至不足以计算容量，即，有多少信息可以通过这种具有长存储器的信道可靠地发送。 本研究攻击这些问题，使用最新的发展领域的信源编码和统计，并增加现有的计算工具，专门为信道与memory.In通信渠道的上下文中，一个适当的模型是最简单的适合的信道输入/输出观测，使足够准确的评估（估计）的信道容量。研究人员正在将普遍的压缩原则，特别是那些为欠采样机制开发的原则，扩展到信息传输问题。该研究的实际推动力包括开发基于模型的容量计算算法。的出发点是有效的实施Baum-Welch/BCJR算法作为一个计算内核的范围内的近似广义Blahut-Arimoto方法。具体来说，利用自适应控制处理状态的数量的技术，权衡每次迭代的时间和计算的准确性。虽然理论推力通过拟合更简单的模型来减少状态空间，但是算法设计组件通过利用马尔可夫链蒙特卡罗技术来导航复杂状态空间，即，通过只穿越高概率状态。

ABSTRACTThe behavior of most physical communication channels depends on the past usage of the channel -- namely, many physical communication channels exhibit "memory". The challenge then is to construct tools that optimally take advantage of the channel memory. In addition, usual information theoretic analysis methods are ill equipped to even compute the capacity, i.e., how much information can be reliably sent through such channels with long memory. This research attacks these problems using recent developments in the fields of source coding and statistics and augments existing computational tools specifically for channels with memory.In the context of communication channels, an adequate model is the simplest fit to the channel input/output observations that enables sufficiently accurate evaluation (estimation) of the channel capacity. The investigators are extending universal compression principles, particularly those developed for the undersampled regime, to information transmission problems. The practical thrust of the research includes the development of algorithms for model based capacity computations. The starting point is the efficient implementation of the Baum-Welch/BCJR algorithm as a computational kernel in a range of approximations to the generalized Blahut-Arimoto method. Specifically, techniques that adaptively control the number of processed states are exploited, trading off the time per iteration and accuracy of computations. While the theoretical thrust reduces the state space by fitting a simpler model, the algorithm design component adds another dimension to complexity reduction by utilizing Markov chain Monte Carlo techniques for navigating complex state spaces, i.e., by transversing only high probability states.