Permutation Group Codebook Generation for Interference-Resistant Channels
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing error-correcting codes struggle to provide reliable communication in power line carrier channels due to multiple interferences like multipath fading, narrow-band noise, and colored background noises, and lack effective construction methods for permutation codes with high error-correcting capabilities.
Innovation Solution
A construction method for (n,n(n−1),n−1) permutation group codes based on coset partition, along with a codebook generator, is developed, featuring a minimum distance of n−1 and error-correcting capability of d−1=n−2, utilizing coset partition and cyclic Latin squares to resist mixed interferences and malicious frequency interferences.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If permutation codes are applied to power line carrier communication, then error-correcting capability is improved, but construction method complexity increases
Solution Approach 1:
The permutation code construction is segmented into coset partitioning, where the code space is divided into multiple cosets based on subgroup relationships. This segmentation allows systematic generation of codewords with guaranteed minimum distance properties, resolving the contradiction by providing a structured approach that improves error-correcting capability while maintaining manageable construction complexity through modular coset-based organization.
Solution Approach 2:
The invention performs preliminary action by pre-defining the coset structure and orbit representatives before actual code construction. The coset partitioning and orbit identification are established in advance, creating a framework that simplifies subsequent codeword generation. This preliminary structuring enables reliable error correction while reducing construction complexity by avoiding ad-hoc code generation.
2Reliability
If algebraic structure design method is used for permutation codes, then error-correcting capability is improved, but executable circuit implementation becomes difficult
Solution Approach 1:
The invention introduces cosets as an intermediary structure between the abstract algebraic design and concrete circuit implementation. The coset representation serves as a mediator that translates complex algebraic operations into simpler, repeatable patterns suitable for hardware implementation. This intermediary structure maintains the error-correcting capabilities derived from algebraic design while enabling practical executable circuit realization through standardized coset-based encoding procedures.
3Object-affected harmful factors
If code with minimum distance n-1 is designed, then anti-interference capability is improved, but code construction complexity increases
Solution Approach 1:
The invention applies local quality by ensuring that each coset within the partitioned code space possesses the required minimum distance property locally. Rather than requiring the entire code construction to be complex, each individual coset is designed with specific structural properties that guarantee the global minimum distance of n-1. This localized approach to quality assurance improves anti-interference capability while keeping individual coset constructions simple and manageable.
Data Source
AI summary
A construction method for a (n,n(n−1),n−1) permutation group code based on coset partition is provided. The presented (n,n(n−1),n−1) permutation group code has an error-correcting capability of d−1 and features a strong anti-interference capability for channel interferences comprising multi-frequency interferences and signal fading. As n is a prime, for a permutation code family with a minimum distance of n−1 and a code set size of n(n−1), the invention provides a method of calculating n−1 orbit leader permutation codewords by On={αo1}α=1n-1(mod n) and enumerating residual codewords of the code set by Pn=CnOn={(l1)n-1On}={(rn)n-1On}. Besides, a generator of the code set thereof is provided. The (n,n(n−1),n−1) permutation group code of the invention is an algebraic-structured code, n−1 codewords of the orbit leader array can be obtained simply by adder and (mod n) calculator rather than multiplication of positive integers. Composition operations of the cyclic subgroup Cn acting on all permutations oα of the orbit leader permutation array On are replaced by well-defined cyclic shift composite operation functions (l1)n-1 and (rn)n-1 so that the action of the cyclic group acting on permutations is realized by a group of cyclic shift registers.