Almost Periodic Function Codes Using Rational Parameters
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Solution Overview
Problem
Existing almost periodic function codes in communication systems, particularly Weyl codes, are optimized using irrational numbers for parameters, which may not be practical for finite code lengths and can lead to suboptimal bit error rates and autocorrelation values.
Innovation Solution
The use of real numbers, specifically parameters represented as δ+(k−1)/K, where δ is a real number between 0 and 1, to determine almost periodic function codes, allowing for optimization of bit error rates and autocorrelation values, even when δ is a rational number, enabling more practical and effective communication.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If irrational numbers are used for parameters in Weyl codes, then the theoretical optimization is achieved, but the practical implementation becomes difficult and suboptimal bit error rates occur
Solution Approach 1:
The patent changes the parameter type from irrational numbers to rational numbers. Specifically, it uses rational numbers with equal intervals (δ+(k−1)/K) to determine almost periodic function codes, replacing the conventional irrational number parameters. This parameter change maintains the optimization effect while enabling practical implementation in digital communication systems.
2Manufacturing precision
If irrational numbers are used for code parameters, then mathematical optimization is achieved, but the autocorrelation values become suboptimal for finite code lengths
Solution Approach 1:
The patent applies parameter changes by using rational numbers with equal intervals instead of irrational numbers. This allows the code parameters to be optimized for finite code lengths, achieving better autocorrelation values that are suitable for practical communication systems with limited code lengths.
3Reliability
If equal intervals are used between code parameters, then the bit error rate is reduced, but the parameters must be irrational numbers which are impractical
Solution Approach 1:
The patent maintains the beneficial equal interval structure (reducing bit error rate) while changing the parameter type from irrational to rational numbers. The rational number parameters with equal intervals (δ+(k−1)/K) achieve both low bit error rates and ease of operation in digital systems.
Data Source
AI summary
The communication method using an almost periodic function code includes using, for modulation, almost periodic function codes the number of which is in accordance with the number of users or the number of channels, among K almost periodic function codes. Where k is an integer from 1 to K and is an identifier for identifying each of the K almost periodic function codes, a parameter that determines each of the K almost periodic function codes is represented by δ+(k−1)/K. The symbol K is N or 2N, where N is a code length of each almost periodic function code. The symbol δ is a real number greater than 0 and less than 1/N.