Autocorrelations of Binary Sequences and Run Structure
Autocorrelations of Binary Sequences and Run Structure
复制标题
二元序列和游程结构的自相关
DOI：
10.1109/tit.2013.2259293
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发表时间：
2012
影响因子：
2.5
通讯作者：
Jürgen Willms
中科院分区：
文献类型：
--
作者：
Jürgen Willms
我们分析了二进制序列的自相关性与其游程结构之间的联系。我们表明，一个二进制序列的周期和非周期自相关可以制定的运行结构。游程结构由序列的连续游程给出。令C =（C 0，C1，...，Cn）表示二进制序列的自相关向量，Δ表示差分算子。我们证明了Δ2（C）的第k个分量可以直接用总长度为k的连续游程来计算。特别是，这表明，第自相关已经确定的所有连续运行的总长度l <; k。在非周期性的情况下，我们展示了如何运行向量可以有效地计算，并给出一个特征的反对称序列在其运行长度编码。
We analyze the connection between the autocorrelation of a binary sequence and its run structure given by the run length encoding. We show that both the periodic and the aperiodic autocorrelation of a binary sequence can be formulated in terms of the run structure. The run structure is given by the consecutive runs of the sequence. Let C = (C0, C1,..., Cn) denote the autocorrelation vector of a binary sequence and Δ the difference operator. We prove that the th component of Δ2(C) can be directly calculated by using the consecutive runs of total length k. In particular, this shows that the th autocorrelation is already determined by all consecutive runs of total length l <; k.In the aperiodic case, we show how the run vector can be efficiently calculated and give a characterization of skew-symmetric sequences in terms of their run length encoding.