RIA: Channel codes for digital communications and storage systems

伊利诺伊大学香槟分校-Urbana Alexander Vardy RIA：用于数字通信和存储系统的信道码信息的可靠传输和存储需要使用纠错信道码来保护数据免受信道噪声或记录介质缺陷引入的错误。纠错码在大多数现代通信和存储系统中实现，从家用光盘播放器到电话线调制解调器、计算机存储器和移动无线电网络，再到卫星和深空通信。在这个项目中，我们使用一种新的动力学方法研究了两种常见的纠错码，即分组纠错码和格码。由于分组码本质上是有限域的子集，而格是具有某些规定距离属性的维实点的离散集合，因此它们通常被视为几何或代数实体。然而，正如刚刚认识到的那样，块和格码也可以被视为动态系统。与传统做法相比，后一种方法有几个深远的优势。目标之一是利用这些优势，试图找到比目前已知的更好的新代码。另一个目标是提供译码复杂度的界限，并开发更高效的最大似然译码器，这大大提高了对于给定译码复杂度可实现的当前性能。此外，我们从理论和实际两个角度研究了分组纠错码和格型纠错码的复杂度和性能之间的精确权衡。沿着这些路线的进展将使通信系统的设计者能够在相同的带宽、功率和复杂性约束下获得更大的编码增益。还处理用于输入受限信道的调制码，该调制码用于将信息编码成该信道允许的特定序列集。这些代码在各种信息存储应用中具有广泛的用途，例如磁或磁光记录系统。目前正在为新兴的全息存储技术开发新的多维调制码。当今使用的大多数调制码都是使用符号动力学中的工具构建的。将分组码视为动态系统的观点使得将代数编码理论的结果应用于调制码的设计变得很自然。我们将使用这种方法来开发更有效的用于全息记录的高阶谱零码和多维调制码的编码器。还将研究在这种调制编码器内集成规定的纠错能力的可能性。

University of Illinois, Champaign-Urbana Alexander Vardy RIA: Channel Codes for Digital Communications and Storage Systems Reliable transmission and storage of information requires the use of error correcting channel codes to protect the data against errors introduced by the channel noise or imperfections of the recording medium. Error correcting codes are implemented in most of the modern communications and storage systems ranging from household compact-disc players through telephone line modems, computer memories, and mobile radio networks to satellite and deep space communications. In this project we investigate two general types of error correcting codes, known as block and lattice codes, using a novel dynamical approach. Since a block code is essentially subset of finite field, while a lattice is a discrete collection of dimensional real points with certain prescribed distance properties, they have been conventionally treated as geometric or algebraic entities. However, as is just now being realized, block and lattice codes may as well be regarded as dynamical systems. The latter approach has several profound advantages over the conventional practice. One of the objectives is to exploit these advantages in an attempt to find new codes, better than presently known. Another objective is to provide bounds on the decoding complexity and develop more efficient maximum-likelihood decoders, which substantially advance the current performance achievable for a given decoder complexity. Furthermore, we study the precise trade-off between complexity and performance in block and lattice error correcting codes, from both theoretical and practical standpoints. Progress along these lines would enable the designer of a communication system to obtain larger coding gains for the same bandwidth, power, and complexity constraints. Also treated are modulation codes for input constrained channels used to encode information into a particular set of sequences admitted by the channel. These codes have widespread use in a variety of information storage applications, such as magnetic or magneto-optic recording systems. New multi-dimensional modulation codes are currently being developed for the emerging technology of holographic storage. Most of the modulation codes in use today are constructed using tools from symbolic dynamics. Taking the point of view of block codes as dynamical systems makes it natural to consider applying results from algebraic coding theory for the design of modulation codes. We will use this approach to develop more efficient encoders for high order spectral null codes and multidimensional modulation codes for holographic recording. The possibility of integrating a prescribed error correcting capability within such modulation encoders will also be studied.