Finite-Field Resource Construction for Multiple Access Systems
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Solution Overview
Problem
The existing multiple access technologies face challenges in efficiently serving more users and improving user performance due to limitations in physical-layer resources, particularly in the wireless communication field.
Innovation Solution
A user-distinguished finite-field resource construction method is introduced, which involves creating finite-field resources by dividing prime field elements into disjoint pairs and constructing extension-field resources, enabling unique sum-pattern mapping and decoding of user symbols, thereby supporting multiple users and improving system reliability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If classical physical resources (time-domain, frequency-domain, code-domain, space-domain) are used for multiple access, then existing multiple access systems can operate, but the number of supported users is limited and user performance cannot be further improved
Solution Approach 1:
The patent changes the mathematical field parameter from complex field to finite field (GF(p)), fundamentally altering the resource representation. By dividing nonzero elements into additive inverse element pairs and using sum-pattern mapping, the system transforms how resources are defined and allocated, enabling support for more users beyond classical resource limitations.
Solution Approach 2:
The patent introduces a new dimension by using finite-field sum patterns as an additional resource differentiation mechanism. Instead of relying solely on traditional time-frequency-code-space dimensions, the system adds a mathematical structure dimension through unique sum-pattern mapping, allowing users to be distinguished by their sum patterns in the finite field.
2Quantity of substance
If more users are served using traditional multiple access technology, then user coverage increases, but resource shortage and performance degradation occur
Solution Approach 1:
The patent segments the finite field resources by dividing nonzero elements into additive inverse element pairs. Each user is assigned a unique sum pattern formed by these segmented pairs, allowing multiple users to share the same physical resources while being distinguished by their unique sum-pattern combinations, thereby maintaining performance while serving more users.
Solution Approach 2:
The system performs preliminary construction of the finite field resource set and establishes unique sum-pattern mapping before actual communication occurs. This pre-configuration ensures that when multiple users transmit simultaneously, their signals can be uniquely decoded based on their pre-assigned sum patterns, preventing performance degradation even as user count increases.
3Quantity of substance
If finite-field resources are constructed with unique sum-pattern mapping, then more users can be supported and decoding is simplified, but the construction complexity increases
Solution Approach 1:
The patent extracts the essential distinguishing feature from complex resource allocation by focusing solely on the sum pattern of additive inverse element pairs. Instead of managing complex multi-dimensional resource assignments, the system extracts and utilizes only the sum pattern property, simplifying the construction process while enabling support for more users.
4Measurement precision
If additive inverse element pairs are used for user distinction, then unique decoding is achieved, but the design becomes more complex compared to classical approaches
Solution Approach 1:
The patent changes the fundamental parameter from complex-valued resources to finite-field elements, which have simpler algebraic properties. The use of additive inverse element pairs in GF(p) provides unique sum patterns that enable accurate decoding, while the finite field arithmetic is computationally simpler than complex field operations, balancing accuracy with implementation complexity.
Data Source
AI summary
The present disclosure relates to the field of communication technologies and in particular to a user-distinguished finite-field resource construction method and a finite-field multiple access system. In order to solve the problem of the limitation of the multiple access resource in the current communication field, the present disclosure employs a user-distinguished finite-field resource construction method to construct a basic-field resource and/or extension-field resource, i.e. finite-field resource. During the use of the finite-field resource, each user sending a binary sequence is assigned one codebook marking symbols that 0 and 1 are respectively mapped into a finite field. The transmitter sends a corresponding finite-field symbol sequence. At the receiver, based on the received finite-field symbols, a finite-field symbol sent by each user can be determined uniquely and thus, a binary symbol sent by each user can be decoded. The present disclosure is applied to the finite-field multiple access system.