Non-linear Feedback Shift Register Gate Reduction
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Solution Overview
Problem
Existing linear feedback shift registers (LFSRs) require a large number of taps and gates to achieve maximal length sequences, which can be inefficient and complex, while non-linear feedback shift registers (NLFSRs) lack a systematic procedure for constructing sequences with guaranteed long periods.
Innovation Solution
A method and system for generating pseudo-random sequences using an NLFSR with a minimal number of gates, employing a feedback logical operation of only one OR gate and one XOR gate, or equivalent, to achieve maximal or near-maximal length sequences by selecting suitable pairs of non-end taps and optimizing their combinations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Duration of action of moving object
If linear feedback shift registers use more taps to achieve maximal length sequences, then the sequence length increases, but the device complexity increases
Solution Approach 1:
The patent changes the fundamental parameter of the feedback function from linear to non-linear. By using non-linear logical operations (AND, OR, NAND, NOR gates) instead of only XOR operations, the system achieves maximal length sequences with fewer taps. For example, a 31-stage register can achieve maximal length with just 3 taps using non-linear feedback, compared to requiring more taps with linear feedback mechanisms.
Solution Approach 2:
The patent combines multiple types of logic gates (AND, OR, NAND, NOR, XOR) in composite feedback configurations to create non-linear feedback functions. This composite approach allows the system to achieve the same sequence length properties as linear systems with many taps, but using fewer physical taps and gates. The composite logic structure replaces the need for numerous XOR gates with a smaller set of diverse gate types.
2Device complexity
If non-linear feedback shift registers use fewer gates, then the device complexity reduces, but the guarantee of long sequence periods is lost
Solution Approach 1:
The patent systematically designs non-linear feedback functions that are guaranteed to produce maximal length sequences. By carefully selecting combinations of logic gates and their connections to specific taps, the system ensures that the feedback produces the desired long-period behavior. The feedback mechanism is not arbitrary but is specifically engineered to achieve maximal length, providing reliability while using fewer gates.
Solution Approach 2:
The patent changes the feedback function parameters from linear to non-linear, which fundamentally alters the system's behavior to achieve both reduced complexity and guaranteed long sequences. The non-linear parameters (using AND, OR, NAND, NOR gates) create feedback characteristics that inherently produce maximal length sequences without requiring the systematic complexity of linear approaches.
3Ease of operation
If linear feedback shift registers use standard XOR operations, then the implementation is simple, but the number of gates required increases
Solution Approach 1:
The patent changes the logical operation parameter from XOR to include AND, OR, NAND, and NOR gates. This parameter change fundamentally reduces the gate count because non-linear operations can achieve the same sequence-generating capability with fewer logical elements. Instead of requiring multiple XOR gates for each tap combination, the system uses fewer non-linear gates to achieve equivalent or superior performance.
Solution Approach 2:
The patent inverts the conventional approach by not using the standard XOR operation for feedback. Instead of applying XOR at each tap position, the system uses non-linear operations that achieve the same purpose with fewer gates. This inversion of the standard method leads to reduced device complexity while maintaining implementation feasibility.
Data Source
AI summary
Provided are a method and system for using a non-linear feedback shift register (NLFSR) for generating a pseudo-random sequence. The method may include generating, for an n-stage NLFSR that requires more than two taps to generate a maximal length pseudo-random sequence, a pseudo-random sequence using a feedback logical operation of only a first logic gate and a second logic gate. Two non-end taps suitable for providing an at least near-maximal length pseudo-random sequence are inputs for the first logic gate, an output of the first logic gate and an end tap are inputs for the second logic gate, and an output of the second logic gate is used as feedback to a first stage of the n-stage NLFSR.