Hexagonal Constellation Decoding via Multiplierless Lookup Tables
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Solution Overview
Problem
Decoding hexagonal constellations in communication systems is complex due to their two-dimensional nature, requiring efficient methods to identify nearest neighbors and compute distances without multiplication, and existing methods are not optimized for practical implementation in transceiver systems.
Innovation Solution
A multiplierless decoding approach is implemented using lookup tables and simplified distance computations, where the Euclidean distance is calculated without multiplication, and likelihood ratios are computed to achieve hard and soft decoding, enabling efficient decoding of hexagonal constellations in communication systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If traditional decoding methods are used for hexagonal constellations, then decoding accuracy can be maintained, but computational complexity increases due to multiplication operations and two-dimensional grid processing
Solution Approach 1:
The patent replaces multiplication-based distance computations with addition-based computations. Instead of calculating Euclidean distance using multiplication (d² = (x1-x2)² + (y1-y2)²), the patent uses a transformed coordinate system where distance can be computed using only addition operations, significantly reducing computational complexity while maintaining decoding accuracy.
Solution Approach 2:
The patent divides the hexagonal constellation decoding into separate processing stages: first transforming the received signal into a new coordinate system, then performing simplified distance computations, and finally identifying nearest neighbors. This segmentation allows each stage to be optimized independently, reducing overall computational burden.
2Productivity
If lookup tables are used for constellation point identification, then decoding speed improves, but memory requirements increase
Solution Approach 1:
The patent creates multiple lookup tables with different resolutions or characteristics tailored to different decoding scenarios. Instead of using a single large lookup table, the system uses several smaller tables optimized for specific constellation regions or signal conditions, reducing overall memory requirements while maintaining fast decoding performance.
3Use of energy by stationary object
If simplified distance computations without multiplication are used, then hardware requirements and power consumption decrease, but decoding precision may be compromised
Solution Approach 1:
The patent applies a coordinate transformation that changes the parameter space in which distance computations are performed. By transforming the received signal coordinates into a new basis, the patent enables distance calculations using only addition operations instead of multiplication, reducing power consumption while preserving the accuracy needed for reliable nearest neighbor identification.
Data Source
AI summary
Embodiments of the invention provide a method of decoding of hexagonal constellations. The decoding methods exploit the inherent structure of the hexagonal grid to eliminate/minimize the requirements for distance computations. A constellation which has unused constellation points is received. A plurality of lookup tables is used for indicating whether a particular constellation point is used. The lookup tables are indexed using the two integers u and v. An initial estimate ū and v is found. The Euclidean distance to the immediate neighbors resulting in the immediate upper and lower integers for ū and v is computed. From the distance to the nearest neighbor, the log-likelihood ratio value is computed.