RIA: Channel codes for digital communications and storage systems

RIA：数字通信和存储系统的通道代码

• 批准号: 9409688
• 负责人: Alexander Vardy
• 金额: $ 10万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9409688&HistoricalAwards=false
• 关键词: RIA; Channel; codes; digital; communications

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.

伊利诺伊大学香槟分校-厄巴纳分校亚历山大·瓦尔迪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码来保护数据不受信道噪声或记录介质缺陷引入的错误的影响。 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的无线电网络，再到卫星和深空通信。 在这个项目中，我们研究两种一般类型的纠错码，称为块和格码，使用一种新的动力学方法。 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度真实的点的离散集合，因此它们通常被视为几何或代数实体。 然而，正如现在所认识到的那样，块码和格码也可以被视为动力系统。 与传统做法相比，后一种方法有几个深刻的优势。 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。 另一个目标是提供解码复杂度的界限，并开发更有效的最大似然解码器，这大大提高了当前的性能，可实现一个给定的解码器复杂度。 此外，我们研究了精确的权衡复杂性和性能的块和格纠错码，从理论和实践的角度来看。 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。 还处理的是用于输入约束信道的调制码，用于将信息编码成由信道接纳的特定序列集。 这些代码广泛用于各种信息存储应用，例如磁或磁光记录系统。 新的多维调制码目前正在开发的全息存储的新兴技术。 今天使用的大多数调制码都是使用符号动力学工具构造的。 把分组码看作是动态系统的观点使得我们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来开发更有效的编码器高阶光谱空码和多维调制全息记录的代码。 还将研究在这种调制编码器中集成规定的纠错能力的可能性。