On the uniqueness of balanced complex orthogonal design

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-09-03 DOI:10.1007/s10623-024-01483-x

Yiwen Gao, Yuan Li, Haibin Kan

引用次数: 0

Abstract

Complex orthogonal designs (CODs) have been used to construct space-time block codes. Its real analog, real orthogonal designs, or equivalently, sum of squares composition formula, have a long history in mathematics. Driven by some practical considerations, Adams et al. (IEEE Trans Info Theory, 57(4):2254–2262, 2011) introduced the definition of balanced complex orthogonal designs (BCODs). The code rate of BCODs is 1/2, and their minimum decoding delay is proven to be \(2^m\), where 2m is the number of columns. We prove, when the number of columns is fixed, all (indecomposable) balanced complex orthogonal designs (BCODs) have the same parameters \([2^m, 2m, 2^{m-1}]\), and moreover, they are all equivalent.

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论平衡复正交设计的唯一性

复正交设计（COD）已被用于构建时空块编码。它的实际类似物--实正交设计，或等价于平方和组成公式，在数学中有着悠久的历史。出于一些实际考虑，亚当斯等人（IEEE Trans Info Theory, 57(4):2254-2262, 2011）提出了平衡复正交设计（BCODs）的定义。BCODs 的码率是 1/2 ，其最小解码延迟被证明为 \(2^m\)，其中 2m 是列数。我们证明，当列数固定时，所有（不可分解的）平衡复正交设计（BCODs）具有相同的参数（[2^m, 2m, 2^{m-1}]），而且，它们都是等价的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.