In order to facilitate the ubiquitous heterogeneous and medium-independent communication networks, transmitter identification is crucial especially as the number of transmitters becomes tremendous in reality. Since the birth of spread-spectrum communications, pseudo-random identification sequences have been widely adopted due to their preferable nearly Dirac-Delta auto-correlation property, which would lead to the advantages in synchronization and multi-user interference mitigation. Maximum-length shift-register sequences (a.k.a. $m$-sequences) are pseudo-random sequences often adopted for multi-access communications, but categorization or grouping of the patterns (bit substrings) contained in $m$-sequences has not been investigated to the best of our knowledge. Thus, this paper is dedicated to the new study on the categorization of $m$-sequences, which would give rise to many applications involving assignment, addressing, and management of identification or spreading sequences. We define new essential parameters, namely single-pattern-searching parameters, and design a new parallel algorithm to spot such inherent parameters associated with each selected underlying pattern. Our proposed new approach will facilitate a highly computationally-efficient solution to find the pattern-attributed (pattern-contained) $m$-sequences without actually generating any $m$-sequence for subsequence-matching between an $m$-sequence and the underlying pattern(s). We further utilize these single-pattern-searching parameters to establish the new analysis of pattern capacity and quality by characterizing multiple pattern attributes within $m$-sequences. The first goal of this work is to find single-pattern-attributed $m$-sequences recursively until the final subset of $m$-sequences is acquired so that each $m$-sequence contains all underlying patterns. The second goal of this work is to find the shortest sequences containing specified patterns. To achieve this goal, we first construct the shortest binary sequences subject to the underlying patterns and it can be accomplished by solving the generalized traveling salesman problem (GTSP). Then, according to the constructed shortest binary sequences, the number of pattern-contained $m$-sequences can be determined thereby. Memory- and computational-complexity analyses are also presented to demonstrate that our proposed new scheme is much more computationally efficient than the conventional subsequence-matching method for searching and counting the pattern-attributed $m$-sequences. On the other hand, our proposed new scheme leads to the same memory-complexity as the conventional method for registering the spotted pattern-attributed $m$-sequences. Finally, three new metrics for assessing the underlying patterns are proposed. They are attributability, discriminability, and ambiguity. The associated numerical evaluation is also provided in this paper.

为了促进无处不在的异构和介质独立的通信网络，发射机识别是至关重要的，尤其是当发射机的数量在现实中变得巨大时。自从扩频通信诞生以来，伪随机识别序列由于其较好的近狄拉克-德尔塔自相关特性而被广泛采用，这将导致同步和多用户干扰抑制方面的优势。最大长度移位寄存器序列（又名$米$-sequences) 是伪随机序列，通常用于多路访问通信，但包含在 $米$-sequences 尚未尽我们所知进行调查。因此，本文致力于对分类的新研究$米$-序列，这将引起许多应用，包括分配、寻址和识别或扩展序列的管理。我们定义了新的基本参数，即单模式搜索参数，并设计了一种新的并行算法来发现与每个选定的基础模式相关联的这些固有参数。我们提出的新方法将促进一个计算效率高的解决方案来找到模式属性（模式包含）$米$- 序列而不实际生成任何 $米$-sequence 用于子序列匹配 $米$-序列和基础模式。我们进一步利用这些单一模式搜索参数，通过表征内的多个模式属性来建立对模式容量和质量的新分析。$米$- 序列。这项工作的第一个目标是找到单模式属性$米$- 递归地排序，直到最后一个子集 $米$-sequences 被获取，以便每个 $米$-sequence 包含所有底层模式。这项工作的第二个目标是找到包含指定模式的最短序列。为了实现这个目标，我们首先构造受底层模式约束的最短二进制序列，它可以通过解决广义旅行商问题（GTSP）来完成。然后，根据构造的最短二进制序列，得到包含模式的个数$米$-序列可以由此确定。还提出了内存和计算复杂性分析，以证明我们提出的新方案比用于搜索和计数模式属性的传统子序列匹配方法在计算上更有效。$米$- 序列。另一方面，我们提出的新方案导致与注册斑点模式属性的传统方法相同的内存复杂性$米$- 序列。最后，提出了三个用于评估潜在模式的新指标。它们是可归因性、可辨别性和歧义性。本文还提供了相关的数值评估。