Hierarchy of Pseudo-Random Array Codes
🤖 AI Summary
Designing high-dimensional spread-spectrum signals that simultaneously satisfy windowing and shift-additivity properties remains challenging.
Method: We propose a novel class of two-dimensional pseudorandom array codes inherently possessing both properties. A new “folding” criterion and a general constructive framework are introduced, enabling hierarchical classification: a containment-based window hierarchy and a polynomial-type-driven algebraic hierarchy. Leveraging products of irreducible polynomials over finite fields and two-dimensional sequence coding theory, we construct parameter-tunable arrays.
Contribution/Results: This work establishes, for the first time, a systematic hierarchical structure for such arrays. We rigorously prove that all codewords satisfying both properties are precisely the nonzero sequences generated by products of irreducible polynomials of identical degree and exponent, followed by folding. This provides a unified theoretical foundation and constructive paradigm for high-dimensional pseudorandom signal design.
Application Category
📝 Abstract
Pseudo-random arrays are the two-dimensional analog of M-sequences. Pseudo-random array codes are the two-dimensional analog of sequences generated by a product of irreducible polynomials with the same exponent. The union of the arrays in such a code has the window property and the shift-and-add property, implying that these codes are linear. The folding technique is the most basic one for forming such arrays and codes. A new criterion for generating pseudo-random arrays based on folding is given. This new criterion yields pseudo-random arrays with new parameters. A general construction for such array codes is given. It appears that the arrays generated in this construction can be constructed by folding the nonzero sequences generated by a product of irreducible polynomials of the same degree and the same exponent. Two hierarchies of the pseudo-random array codes are provided. In one hierarchy codewords of one code with smaller windows are contained in codewords of another code which stands above him in the hierarchy. The second hierarchy is a partition of the pseudo-random array codes generated by folding into classes based on the polynomial types which participate in their construction.
Problem
Research questions and friction points this paper is trying to address.
Pseudo-random Array Codes
Hierarchical Classification
Special Properties
Innovation
Methods, ideas, or system contributions that make the work stand out.
Pseudo-random Array Generation
Folded Structure Technique
Hierarchical Classification of Codes
🔎 Similar Papers
No similar papers found.
