Lattice Signal Modulation With Generalized Polar Code Decoding
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Solution Overview
Problem
Existing communication technologies lack efficient methods for combining generalized bit-to-symbol and symbol-to-bit maps with forward error correction (FEC) in wireless digital communications, particularly for arbitrary finite abelian groups and lattice-based signal constellations, without practical implementations or measurable gains.
Innovation Solution
A method involving generalized polar codes is applied to abelian group elements, mapping them to lattice-based signal constellations, and using successive cancellation for decoding, integrating bit-to-symbol and symbol-to-bit maps with FEC to enhance error correction and modulation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If generalized polar codes are applied to abelian group elements with lattice-based signal constellations, then error correction capability is improved, but device complexity increases
Solution Approach 1:
The encoding process is segmented into distinct functional blocks: bit-to-symbol mapping module, generalized polar code application module, and symbol-to-bit mapping module. The decoding process is similarly segmented with separate modules for receiving signals, applying successive cancellation decoding, and mapping results. This modular segmentation allows each component to be optimized independently while maintaining overall system reliability.
Solution Approach 2:
Abelian group elements serve as intermediaries between binary input strings and lattice-based signal constellation points. The generalized polar codes operate on these abelian group elements, which act as a mathematical mediator that enables the transformation from discrete binary data to continuous signal space while preserving error correction properties. This intermediary structure simplifies the overall transformation process.
2Productivity
If dense lattice constellations are used for modulation, then throughput is increased, but energy consumption increases
Solution Approach 1:
The system enables dynamic adjustment of coding rates in the generalized polar codes, allowing optimization of the balance between throughput and energy consumption. By changing the coding rate parameter, the system can adapt to different channel conditions and power availability, achieving higher throughput when energy is abundant and maintaining reliability when energy is constrained.
Solution Approach 2:
The encoding and decoding apparatus are designed to adaptively select modulation schemes and coding parameters based on channel conditions. This dynamic adaptation allows the system to maximize throughput under favorable conditions while conserving energy under poor channel conditions or power constraints, resolving the contradiction between throughput and energy consumption.
Data Source
AI summary
A signal receiver receives a signal that encodes symbols. Each symbol represents a binary string encoded using a generalization of polar codes. The signal receiver identifies, based on the symbols, a data structure representing at least one probability of transmission. The signal receiver includes a decoder that decodes the signal based on the data structure to identify the binary strings encoded by the generalization of polar codes.