Finite Field Channel Allocation Matrices for Complete User Connectivity
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for allocating channels in communication systems among multiple users, such as radio stations, fail to minimize the refresh period while ensuring each user communicates with every other user at least once, especially in dense environments, leading to inefficiencies and leftover unconnected pairs.
Innovation Solution
The method generates channel allocation matrices using finite field theory to optimize channel assignments, ensuring each user is connected to every other user within a minimum number of sessions by utilizing channels that are assigned based on unique slopes and partitions, allowing for efficient data exchange across multiple time slots.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If pseudo-random assignment rule is used for channel allocation, then channel assignments are generated, but the refresh period is not minimized and some user pairs remain unconnected
Solution Approach 1:
The patent transforms the channel allocation problem from random assignment to a structured mathematical problem using finite field parameters. By representing users as points (x,y) in a finite field Fq² and channels as lines with specific slopes and intercepts, the system guarantees that every pair of users shares a channel exactly once, minimizing the refresh period to t=q+1 sessions while ensuring complete connectivity.
Solution Approach 2:
The patent segments the set of users into structured groups based on their coordinates in the finite field plane. Each session partitions users into groups that share specific channel characteristics (slope and intercept), ensuring systematic coverage of all user pairs without redundancy or omission.
2Productivity
If successive transmission on a single logical channel is used, then users within radio range receive the same information simultaneously, but no additional useful information is transmitted
Solution Approach 1:
The patent introduces an additional dimension to channel identification by using both slope (a) and intercept (b) parameters from the linear equation y=ax+b. This two-dimensional channel space allows simultaneous transmissions to be distinguished not just by time slot but by their geometric relationship in the finite field plane, enabling cooperative relaying where users can identify and retransmit information from multiple sources.
3Reliability
If the number of sessions is increased to ensure all user pairs connect, then connection completeness improves, but the refresh period increases beyond the theoretical limit
Solution Approach 1:
The patent performs preliminary organization of users into a finite field coordinate system before channel allocation begins. By pre-assigning users to points (x,y) and defining channels as lines with specific slopes and intercepts, the system ensures that the minimum necessary number of sessions (t=q+1) is sufficient to guarantee every pair connects exactly once, achieving the theoretical combinatorial limit.
Data Source
Figure 1~2
Figure 3~4
AI summary
The invention relates to a method and a device for allocating communication channels to several users in a network, comprising at least the following steps: a) defining a first allocation set composed of the following triplets (channel number, slot number, user assigned to a channel for a given slot) representing the allocation of C communication channels, for the N users, over a time session composed of several time slots, respecting C=N and C=cardinal of a finite field, b) generating from the first channel allocation matrix, C other matrices, said C allocation matrices being generated using a function so that each user sees the other users at least once during the session.