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首页> 外文期刊>IEEE Transactions on Information Theory >Extended Closed-Form Expressions for the Robust Symmetrical Number System Dynamic Range and an Efficient Algorithm for Its Computation
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Extended Closed-Form Expressions for the Robust Symmetrical Number System Dynamic Range and an Efficient Algorithm for Its Computation

机译：鲁棒对称数系统动态范围的扩展闭式表达式及其有效算法

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摘要

The robust symmetrical number system (RSNS) is a number theoretic transform based on $Ngeq 2$ sequences that can extract the maximum amount of information from symmetrical folding waveforms. The sequences, based on coprime moduli, exhibit an integer gray code property making the RSNS well suited for many applications that benefit from an inherent error detection and correction capability, such as analog-to-digital converters, direction finding arrays, and radar waveform design. To use the RSNS, it is necessary to know the greatest length of combined sequences without ambiguities, called the dynamic range $widehat{M}$, for which only a few closed-form expressions currently exist. In this paper, an efficient algorithm for computing $widehat{M}$ and its position within the combined set of sequences is presented and shown to be independent of the size of the moduli. The algorithm is used to generate the equations for several groups of additional moduli arrangements. Closed-form expressions for $widehat{M}$ are conjectured and proved using the obtained congruence equations that define the ambiguity locations.
机译：鲁棒对称数系统（RSNS）是基于$ Ngeq 2 $序列的数论变换，可以从对称折叠波形中提取最大量的信息。这些基于互质数模的序列具有整数格雷码特性，这使得RSNS非常适合许多应用，这些应用得益于固有的错误检测和纠正功能，例如模数转换器，测向阵列和雷达波形设计。为了使用RSNS，有必要知道最大长度的组合序列而没有歧义，称为动态范围$ widehat {M} $，目前仅针对其中的几种闭式表达式。在本文中，提出了一种有效的算法，用于计算$ widehat {M} $及其在序列组合集合中的位置，并显示出与模数大小无关。该算法用于生成几组附加模态布置的方程式。使用获得的定义歧义位置的等式方程，推测并证明了$ widehat {M} $的闭式表达式。

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