CIF: Small: A New Coding Paradigm for Communication Over Broadcast Channels Using Nested Linear Codes: A Duality of Structure and Randomness

在最近的过去，出现了一些需要大规模部署通信网络基础设施的应用场景，例如分组交换有线网络、移动蜂窝无线网络和分布式传感器网络。在这个项目中，解决了多终端系统中信息的有效通信问题，其中多用户信道必须在网络中的几个用户之间共享。这个项目中开发的新编码方法揭示了抽象群体的复杂结构方面。高效编码技术的发展对下一代通信网络有着广泛的影响。在本项目中，研究了基于由嵌套线性码构造的新的多用户码集的一类网络通信问题的统一框架的开发。特别地，考虑了在一般离散无记忆广播信道上传输信息的问题。在过去的三十年里，这个问题受到了极大的关注。然后将该方法应用于其他多用户信道，例如干扰信道。对于这些问题，嵌套线性代码集成的平均性能严格优于标准非结构化代码集成。考虑利用现有技术开发一种方法来有效地计算这类编码方案(有限维但非凸优化问题)的性能极限。该项目还考虑开发具有计算效率的编码和解码算法和程序的实际代码构造。这是通过对这些码的生成器和奇偶校验矩阵施加额外的稀疏性约束来实现的。

In the recent past, several application scenarios have emerged that require large-scale deployment of communication network infrastructure such as packet-switched wireline networks, mobile cellular wireless networks, and distributed sensor networks. In this project, the problem of efficient communication of information in multiterminal systems, where a multiuser channel must be shared among several users in the network is addressed. The new coding methods developed in this project shed light on intricate structural aspects of abstract groups. The development of efficient coding techniques has broad impact on the next generation of communication networks. In this project, the development of a unified framework to address a class of network communication problems based on new multiuser code ensembles constructed from nested linear codes is studied. In particular, the problem of transmission of information over general discrete memoryless broadcast channels is considered. This problem has received a great deal of attention in the last thirty years. This approach is then applied to other multiuser channels such as the interference channel. For these problems, the average performance of nested linear code ensembles is strictly better than that of the standard unstructured code ensembles. The development of a methodology to compute the performance limits of such coding schemes (which are finite dimensional yet non-convex optimization problems) efficiently with current technology is considered. This project also considers the development of practical constructions of codes with computationally efficient encoding and decoding algorithms and procedures. This is accomplished by putting additional sparsity constraints on the generator and parity-check matrices of these codes.