Universal Source and Channel Codes for Non-Ergodic Channels

当模拟源（如音频或视频信号）通过噪声信道传输时，通常首先对源进行量化和压缩（源编码），然后对源进行编码，使其对噪声信道具有鲁棒性（信道编码）。对于一类称为遍历信道的信道，最好分别执行源和信道编码。这一原则已经成为设计一些现代通信系统的工程指导原则。然而，在一些实际的通信系统中，例如在向许多用户广播一个源时，会遇到非遍历信道。对于这类通道，基于分离的方法不一定是最佳的。这项工作的重点是理解和提供为这些信道执行源和信道编码的指导方针。考虑了非遍历信道编码中三个独立但相关的问题。第一个是最小化端到端失真的测量，例如在非遍历噪声信道上通信源的预期均方误差。重点是模拟和混合模拟到数字联合源信道编码技术的设计，它可以优于传统的基于分离的数字方法。研究了具有记忆的非遍历信道的实用通用信道码的设计，表明编码决策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，考虑了底层关联模型不完全已知的分布式压缩通用码的设计。除了标准的教育活动外，更广泛影响的一个关键方面是为我们的学生与其他大学的研究人员互动创造了途径。

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.