CIF: Small: Optimal Coded Modulation When Asymmetric Signaling Achieves Capacity

该项目开发了必要的理论框架，以实现在某些数据通信信道上，在使用低复杂性实用解码器的同时，尽可能高的可靠数据速率。应用包括使用自由空间光通信或射频通信的卫星通信。实际上，所有的数据都是通过发送作为波形在物理信道上传输的符号序列来通信的。这些符号通常决定波形的幅度和/或相位，通常是从可能值的离散字母表中绘制的。传统上，符号字母是对称的。例如，如果有一个符号的幅度为+5伏，那么也会有一个符号的幅度为-5伏。对于对称字母，有多种现有的编码调制技术，可以使用实用的解码器实现高数据速率。然而，对于包括普通卫星频道在内的重要频道，最好的字母表不是对称的。这使得实现最高速率的编码调制和相关解码算法的设计都变得非常复杂。该项目开发了一种技术，可以在不需要对称的情况下识别字母符号的最佳位置，并引入了一种新的编码调制形式，称为概率排列整形，它可以实现最高的数据速率，同时仍然允许实际解码器使用最佳的非对称字母。这项研究的成功成果的实际影响将导致地球-空间的高速卫星连接，反之亦然。该项目利用概率排列整形，即使在最佳输入分布不对称的情况下，也可以使用实用的低密度奇偶校验（LDPC）解码器接近信道容量。这种方法避免了多层编码和多级解码的复杂性和错误传播。它还避免了与联合解映射和解码相关的延迟和性能损失。该项目还开发了一系列新的优化技术，利用Blahut-Arimoto算法的修改，动态地重新分配质量点的位置。动态分配Blahut-Arimoto不仅描述了特定信噪比下的点解，而且还描述了最小基数最优有限支持分布的整个演变，因为信道容量在整个感兴趣的范围内增加。在这些有限支持分布族的背景下，它们本质上是不对称的，概率排列整形建立在现有的概率幅度整形框架上，提供灵活实用的编码调制解决方案，支持整个非均匀分布族，这在以前被认为是外来的。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project develops the theoretical framework necessary to achieve, on certain data communication channels, the highest possible reliable data rate while still using low-complexity practical decoders. Applications include satellites communicating using either free-space optical communication or radio-frequency communication. Practically all data is communicated by sending a sequence of symbols transmitted as a waveform over a physical channel. These symbols often determine the amplitudes and/or phases of the waveform and are typically drawn from a discrete alphabet of possible values. Traditionally, symbol alphabets are symmetric. For example, if there is a symbol with an amplitude of +5 volts there will also be a symbol with an amplitude of -5 volts. For symmetric alphabets, there are a variety of existing coded modulation techniques that achieve high data rates using practical decoders. However, for important channels including common satellite channels, the best alphabets turn out not to be symmetric. This significantly complicates the design both of the coded modulation to achieve the highest rates and of the associated decoding algorithms. This project develops techniques that identify the optimal placement of alphabet symbols without requiring symmetry and introduces a new form of coded modulation, known as probabilistic permutation shaping, that achieves the highest possible data rates while still allowing practical decoders to use the optimal asymmetric alphabets. The practical impact from a successful outcome of this research will lead to high-speed satellite links for both earth-space and vice-versa.This project utilizes probabilistic permutation shaping, which approaches channel capacity using a practical low-density parity check (LDPC) decoder even when the optimal input distribution is asymmetric. This approach avoids the complexity and error propagation of multi-layer coding with multi-stage decoding. It also avoids the latency and performance loss associated with joint de-mapping and decoding. The project also develops a family of new optimization techniques utilizing a modification of the Blahut-Arimoto algorithm that dynamically re-assigns the positions of mass points. Dynamic-assignment Blahut-Arimoto characterizes not only point solutions at a specific signal-to-noise ratio, but the entire evolution of the minimal cardinality optimal finite-support distributions as the channel capacity increases over the entire range of interest. In the context of these families of finite-support distributions, which are inherently asymmetric, probabilistic permutation shaping builds on the existing framework of probabilistic amplitude shaping to provide flexible and practical coded modulation solutions that support entire families of non-uniform distributions that would have previously been considered exotic.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.