RIA: Channel codes for digital communications and storage systems

伊利诺伊大学香槟分校Alexander Vardy RIA：数字通信和存储系统的信道代码信息的可靠传输和存储需要使用纠错信道代码来保护数据免受信道噪声或记录介质缺陷引入的错误。纠错码应用于大多数现代通信和存储系统，从家用光盘播放机到电话线调制解调器、计算机存储器和移动无线网络，再到卫星和深空通信。在这个项目中，我们研究了两种一般类型的纠错码，即块码和点阵码，使用一种新的动态方法。由于分组码本质上是有限域的子集，而晶格是具有一定规定距离属性的维度实点的离散集合，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，块码和点阵码也可以看作是动力系统。与传统做法相比，后一种方法有几个深刻的优点。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。另一个目标是提供解码复杂性的界限，并开发更有效的最大似然解码器，这将大大提高给定解码器复杂性下当前可实现的性能。此外，我们从理论和实践的角度研究了块纠错码和点阵纠错码的复杂性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、功率和复杂性限制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，用于将信息编码成信道所允许的一组特定序列。这些代码在各种信息存储应用中广泛使用，例如磁或磁光记录系统。新的多维调制码目前正在开发用于新兴的全息存储技术。目前使用的大多数调制码都是使用符号动力学工具构建的。从分组码作为动态系统的角度出发，可以很自然地考虑将代数编码理论的结果应用于调制码的设计。我们将使用这种方法开发更高效的编码器，用于高阶频谱零码和全息记录的多维调制码。在这样的调制编码器内集成规定的纠错能力的可能性也将被研究。

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.