Encoding method and encoder for (n,n(n-1),n-1) permutation group code in communication modulation system
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Solution Overview
Problem
Current communication systems lack effective mapping encoding algorithms and specific executable schemes for permutation group codes, particularly in PGC-MFSK coded modulation transceivers, due to the absence of algebraic encoding and decoding schemes, leading to inefficiencies in resisting multipath fading and multi-user interference.
Innovation Solution
An encoding method and encoder for (n, n(n−1), n−1) permutation group codes based on coset partition are developed, which map k-length binary information sequences to n-length permutation codewords, utilizing coset characteristics to achieve ultra-low delay and error-correcting capabilities, and are integrated into a communication modulation system to form a time-diversity and frequency-diversity channel access technology.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a (n, n(n-1), n-1) permutation group code is utilized to control the carrying signal with time diversity and frequency diversity, then the capability for resisting multipath fading and multi-user interference is improved, but the system complexity increases due to the lack of algebraic encoding and decoding schemes
Solution Approach 1:
The patent transforms the permutation group code encoding problem into a parameter-based algebraic computation system. By defining specific parameters (n, k, coset partition structures) and algebraic operations (coset leader identification, syndrome calculation, parity-check matrix multiplication), the system achieves systematic encoding that reduces complexity while maintaining the reliability benefits of time and frequency diversity.
Solution Approach 2:
The patent replaces the mechanical/random permutation selection approach with an algebraic computation system. Instead of using random permutation codes or complex search-based encoding, the invention uses algebraic structures (coset partition, parity-check matrices, syndrome calculation) to systematically generate and select codewords, thereby reducing system complexity while preserving error-correcting capabilities.
2Ease of manufacture
If random permutation code is used due to the lack of algebraic encoding schemes, then the implementation is simplified, but the error-correcting capability and mapping efficiency are reduced
Solution Approach 1:
The patent segments the code set into cosets with distinct algebraic structures. By dividing the permutation group code into multiple cosets (each with its own coset leader and parity-check properties), the system enables systematic encoding through algebraic operations while maintaining implementation simplicity. This segmentation allows for efficient coset-based encoding that outperforms random permutation codes.
Solution Approach 2:
The patent introduces specific algebraic parameters (coset partitioning, parity-check matrices, syndrome values) that transform the encoding process from random selection to structured computation. These parameter-based algebraic operations enhance error-correcting capability while keeping the implementation straightforward through systematic calculation procedures.
3Productivity
If 2k codewords are selected from n(n-1) codewords to match 2k k-length binary information sequences, then the mapping efficiency is improved, but the encoding complexity increases without an effective mapping encoding algorithm
Solution Approach 1:
The patent replaces the manual or random codeword selection process with an algebraic computation system. By using parity-check matrices, syndrome calculation, and coset leader identification algorithms, the system automatically and efficiently maps k-length binary information sequences to appropriate codewords from the n(n-1) available options, achieving high mapping efficiency with systematic complexity management.
Solution Approach 2:
The patent uses algebraic parameters (coset indices, syndrome values, parity-check matrix entries) to systematically determine which 2k codewords to select from the n(n-1) available codewords. This parameter-based approach creates an efficient one-to-one mapping between binary information sequences and selected codewords, improving productivity while managing encoding complexity through structured algebraic operations.
Data Source
AI summary
The present disclosure provides an encoding method and an encoder for a (n, n(n−1), n−1) permutation group code in a communication modulation system, in which 2k k-length binary information sequences are mapped to 2k n-length permutation codeword signal points in a n-dimensional modulation constellation Γn. The constellation Γn with the coset characteristics is formed by selecting 2k n-length permutation codewords from n(n−1) permutation codewords of a code set Pn,x<sub2>i </sub2>of the (n, n(n−1), n−1) permutation group code based on coset partition. The constellation Γn is a coset code in which 2k<sub2>1 </sub2>cosets are included and each coset includes 2k<sub2>2 </sub2>permutation codewords, where k=k1+k2, and 2k≤n(n−1). The present disclosure utilizes the coset characteristics to realize one-to-one correspondence mapping of the binary information sequence set to the permutation code constellation, so that the time complexity of executing the encoder is at most the linear complexity of the code length n.