Permutation Group Code Decoding for Interference-Resistant MFSK
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Solution Overview
Problem
Current PGC-MFSK coded modulation transceiver systems lack effective decoding algorithms and specific decoder implementations for permutation group codes, particularly for (n, n(n−1), n−1) permutation group codes, which are essential for robust communication in interference-prone environments like power line and wireless channels.
Innovation Solution
A complete algebraic decoding method and decoder are provided for (n, n(n−1), n−1) permutation group codes, utilizing an intermediate parameter w to calculate and arrange code elements, enabling correct decoding even with mixed interferences and deep fading, with a focus on low complexity and high accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a random permutation code is used in PGC-MFSK coded modulation system, then the system can be implemented without algebraic coding schemes, but the system lacks effective decoding algorithms and has poor anti-interference capability
Solution Approach 1:
The patent applies parameter changes by transforming the permutation code into an algebraic structure with specific parameters (n, n(n-1), n-1) where n is a prime number. This algebraic formulation enables the development of effective decoding algorithms while maintaining the code's anti-interference capabilities through structured mathematical properties.
Solution Approach 2:
The patent introduces an intermediary algebraic structure (the (n, n(n-1), n-1) permutation group code) that bridges the gap between random permutation codes and effective decoding algorithms. This algebraic framework serves as a mediator that enables systematic decoding while preserving the robustness against multipath fading and interference.
2Reliability
If a complete algebraic decoding method is implemented for (n, n(n-1), n-1) permutation group code, then the system achieves strong anti-interference capability and correct decoding under mixed interferences, but the decoder complexity increases
Solution Approach 1:
The patent segments the decoding process into distinct algebraic steps: determining the intermediate parameter w by solving (r1-r2)w=(s1-s2)(mod n), calculating code elements using p(i)=(s1+(n-r1+i)w)(mod n), and constructing the decoded codeword. This segmentation makes the complex algebraic decoding process more manageable and implementable.
Solution Approach 2:
The patent replaces traditional mechanical or heuristic decoding approaches with algebraic operations. By substituting algebraic structures and mathematical operations for conventional decoding methods, the system achieves reliable decoding under interference while maintaining computational efficiency through standardized algebraic procedures.
3Reliability
If the (n, n(n-1), n-1) permutation group code is combined with MFSK modulation, then the system has strong robustness to multiple mixed interferences, but the data transmission rate is limited
Solution Approach 1:
The patent changes the code parameters to (n, n(n-1), n-1) where the code length is n, minimum distance is n-1, and cardinality is n(n-1). This parameter optimization achieves the best balance between error-correcting capability (d-1=n-2) and transmission efficiency, allowing robust communication at low to moderate data rates in interference-prone environments.
Data Source
AI summary
The disclosure discloses an algebraic decoding method and a decoder for a (n, n(n−1), n−1) permutation group code in a communication modulation system. The basic principle of the decoding method is: assuming that two code elements p(r1)=s1 and p(r2)=s2 can be correctly detected in a received real vector with a length of n, including their element values s1, s2 and position indices r1, r2 in the vector, an intermediate parameter w is determined by solving an equation (r1−r2)w=(s1−s2)(mod n); and each code element is calculated by w according to p(i)=(s1+(n−r1+i)w)(mod n), i=1, 2, . . . , n. The decoder is mainly composed of multiple n-dimensional registers, a w calculator, n code element calculators, and a code element buffer. In the disclosure, in a case where a receiver only correctly detects two code elements in a transmitted codeword with a length of n, the codeword can be correctly decoded by using the received information of the two code elements.