Towards a Basic Understanding of Channels with Synchronization Errors

传统通信系统中的一个基本假设是发送器和接收器是同步的：对于每个发送的符号，一个人接收一个信道输出样本。这一假设在高信噪比状态下是有效的，在高信噪比状态下，定时误差通常可以近乎完美地被跟踪。随着过去十年的新编码技术导致信噪比大大降低，这一假设不再有效；在许多应用中，同步是一个日益重要的问题。在未来的几年里，随着基本信道的实用近容量编码成为低信噪比条件下的标准，这很可能成为实际系统中的瓶颈。尽管如此，具有同步误差的信道，甚至包括最简单的随机删除信道，都是信息论中一个明显未被研究的领域。虽然存在用于具有差错的基本信道的实用的近容量码族，例如二进制对称信道和加性高斯白噪声(AWGN)信道，但甚至没有已知的可证明的删除信道容量的表达式，更不难的是具有同步的信道的更困难的变化。这代表着现代信息理论中的一个根本鸿沟。这项研究包括通过扩展信息理论基础和设计新的编码和编码/解码技术来推进具有同步误差的信道的编码的最新技术。i

A basic assumption in classical communications systems is that the transmitter and receiver are synchronized: for each transmitted symbol, one receives one channel output sample. This assumption has been valid under high signal-to-noise ratio regimes, where timing errors can generally be tracked nearly perfectly. With the new coding techniques of the last decade, leading to much lower signal-to-noise ratios, this assumption is no longer valid; synchronization is an increasingly important issue in many applications. It is likely to become a bottleneck in real systems in the years to come, as practical near-capacity codes for basic channels become standard under low signal-to-noise regimes.Despite this, channels with synchronization errors, including even the simplest random deletion channel, represent a remarkably under-studied area in information theory. While there are families of practical near-capacity codes for basic channels with errors, such as the binary symmetric channel and the additive white Gaussian noise (AWGN) channel, there is not even a known provable expression for the capacity of the deletion channel, much less more difficult variations of channels with synchronization. This represents a fundamental gap in modern information theory. This research involves advancing the state of the art in coding for channels with synchronization errors, both by expanding on the information-theoretical foundations and by designing new codes and coding/decoding techniques.i