Perturbation Codes: A New Class of Linear Convolutional Codes

扰动码：一类新的线性卷积码

• 批准号: 0830381
• 负责人: John Kieffer
• 金额: $ 11.5万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0830381&HistoricalAwards=false
• 关键词: Perturbation; Codes; New; Class; Linear

Abstract for NSF Proposal 0830381Project Title: Perturbation Codes: A New Class of LinearConvolutional CodesLinear convolutional codes are widespread in data communication systems and datastorage systems. Each such code processes data at a ¯xed rate and with a ¯xed delay, so thatthe fraction of errors (called average distortion) in the reconstructed data will be acceptablysmall. The primary problem of linear convolutional code design is to ¯nd an optimal code,which is a code yielding the minimum average distortion among codes in a ¯nite set of feasiblecodes. In most cases, with past techniques, this problem could only be solved approximately,yielding an almost optimal code (a code with near minimum average distortion), the set offeasible codes being too large for the average distortion of codes to be examined individually.In this project, we investigate a new technique, called perturbation theory, which reduces theset of feasible codes to a much smaller set of codes called perturbation codes. In many cases,an optimal code will be one of the perturbation codes, and it can be found in a reasonableamount of time.Each linear convolutional code in the set of feasible codes is described via a parity checkmatrix over the binary ¯eld, consisting of a ¯xed number of rows and columns. A perturba-tion class of codes consists of codes whose parity check matrices can be arranged so that acertain number of rows at the top remain ¯xed. Any code will lie in more than one pertur-bation class of codes, depending upon which rows of the parity check matrix are held ¯xed.Under certain conditions, there will be a natural group acting on the parity check matricesof a perturbation class of codes. Using the group structure, a subset of each perturbationclass of codes is selected. A code will be declared to be a perturbation code if it is among theselected codes in a certain number of perturbation classes containing the code. There is °ex-ibility in the de¯nition of perturbation code. In this project, we investigate how to properlydelineate the perturbation code concept so that an optimal code can be found from amonga small set of perturbation codes, for source and channel models of su±cient symmetry.

NSF提案的摘要0830381Project标题：扰动代码：一类新的线性验证代码线性卷积代码在数据通信系统和数据设备系统中广泛。每个这样的代码都以``X的速率''处理数据，并以延迟的延迟处理，因此，重建数据中错误的部分（称为平均失真）将被接受为小。线性卷积代码设计的主要问题是``最佳代码''，该代码是在一组可行的代码集中产生的代码，在代码之间产生最小的平均失真。在大多数情况下，使用过去的技术，只能解决此问题，得出几乎最佳的代码（具有接近最低平均失真的代码），设置的不可避免的代码太大了，无法单独检查的平均代码的平均代码。我们调查了一个新技术，称为“启动理论”，该理论可降低代码的theset codes，该代码范围是可行的代码。在许多情况下，最佳代码将是扰动代码之一，并且可以在合理的时间内找到它。通过二进制的平等checkmatrix在二进制上描述了一组可行代码中的线性卷积代码，由二进制文件列出，由XED的行数和列组成。一类代码类别由代码组成，其代码可以安排奇偶校验校验，以使顶部的一排行数保持在X左右。任何代码都将在多个扰动类别的代码类别中，具体取决于均等检查矩阵的哪一行。在某些条件下，将有一个自然组作用于奇偶校验检查矩阵的扰动类别代码。使用组结构，选择了每个代码的每个扰动类别的子集。如果代码在包含代码的一定数量的扰动类中所选代码之一，则将被声明为扰动代码。该项目中有°的能力，我们研究了如何正确地描述扰动代码概念，以便可以从少量的扰动代码中找到最佳代码，以实现SU±CIENT对称性的源和信道模型。