Universal Source and Channel Codes for Non-Ergodic Channels

当通过噪声信道传输诸如音频或视频信号的模拟信源时，通常首先对信源进行量化和压缩(信源编码)，然后进行编码以使其对噪声信道(信道编码)具有健壮性。对于一类称为遍历信道的信道，分别执行信源和信道编码是最佳的。这一原则已经成为设计几个现代通信系统的工程指导方针。然而，在几个实际通信系统中遇到非遍历信道，例如在向许多用户广播信源时。对于这类信道，基于分离的方法不一定是最优的。这项工作的重点是理解和提供对这种信道执行信源和信道编码的指导方针。第一种是最小化端到端失真的度量，例如在非遍历噪声信道上通信信源时的预期均方误差。重点是设计模拟和混合模拟-数字联合信源-信道编码技术，其性能优于传统的基于分离的数字方法。然后讨论了具有记忆的非遍历信道的实用通用信道码的设计，结果表明编码判决反馈信号处理是解决这些问题的一种很有前途的技术。最后，在底层相关模型不完全已知的情况下，考虑了用于分布式压缩的通用代码的设计。除了标准的教育活动，更广泛的影响的一个关键方面是为我们的学生创建与来自其他大学的研究人员互动的途径。

When an analog source such as an audio or video signal is transmitted over a noisy channel, typically the source is first quantized and compressed (source coded) and then encoded to make it robust to the noisy channel (channel coded). For a class of channels called ergodic channels, it is optimal to separately perform source and channel coding. This principle has served as an engineering guideline to design several modern communication systems. However non-ergodic channels are encountered in several practical communication systems, for example in broadcasting a source to many users. For this class of channels, the separation based approach is not necessarily optimal. The focus of this work in understanding and providing guidelines for performing source and channel coding for such channels.Three separate but related problems in coding for non-ergodic channels are considered. The first is that of minimizing a measure of end-to-end distortion such as expected mean squared error in communicating a source over a non-ergodic noisy channel. The focus is on the design of analog and hybrid analog to digital joint source-channel coding techniques which can outperform conventional separation based digital approaches. Then the design of practical universal channel codes for non-ergodic channels with memory is considered and it is shown that coded decision feedback signal processing is a promising technique to solve these problems. Finally, the design of universal codes for distributed compression where the underlying correlation model is not perfectly known is considered.Apart from standard educational activities, a key aspect of the broader impact is in creating avenues for our students to interact with researchers from other universities.