Geometric Signal Constellations for Higher-Capacity SNR-Limited Links
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Solution Overview
Problem
Existing communication systems face a significant gap in capacity compared to the theoretical Shannon Gaussian limit due to the use of constellations that are not optimally designed, leading to inefficiencies in bandwidth and power usage.
Innovation Solution
The development of unequally spaced geometrically shaped constellations that maximize capacity measures such as parallel decode (PD) and joint capacity, using techniques like LDPC and Turbo codes, to reduce the gap between practical constellations and the Gaussian channel capacity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional constellations that maximize minimum distance (dmin) are used, then reliability is improved through better error performance, but capacity is reduced leading to a significant gap from the Shannon Gaussian limit
Solution Approach 1:
The patent changes the fundamental parameter of constellation design from maximizing minimum distance to optimizing capacity measures such as parallel decode capacity and joint capacity. This involves transforming the constellation points to unequally spaced geometric shapes that maximize the mutual information between transmitted and received signals, thereby closing the gap to the Shannon Gaussian limit while maintaining reliability through capacity-optimized point distributions
Solution Approach 2:
The patent introduces new dimensional considerations by optimizing constellations in terms of capacity measures rather than just geometric distance. This involves evaluating constellations based on parallel decode capacity and joint capacity dimensions, which are information-theoretic measures that capture the effective data transmission capability beyond simple Euclidean distance metrics
2Ease of manufacture
If equal probability symbol transmission is used in practical constellations, then implementation simplicity is maintained, but capacity is reduced compared to the theoretical Gaussian distribution
Solution Approach 1:
The patent applies local quality by creating unequally spaced constellation points where different regions of the constellation have different spacing characteristics. This allows the system to maintain simple equal probability symbol transmission while achieving capacity optimization through strategically placed constellation points that maximize information transmission in different local regions of the signal space
3Ease of manufacture
If finite practical constellations are used instead of theoretical Gaussian distribution, then system implementation becomes feasible, but capacity is reduced below the Shannon limit
Solution Approach 1:
The patent creates practical finite constellation copies that approximate the theoretical Gaussian distribution's capacity characteristics. By designing unequally spaced geometric constellations that capture the essential information-theoretic properties of the Gaussian channel, the system achieves implementation feasibility while maintaining capacity close to the Shannon limit through optimized finite point distributions
Data Source
AI summary
Communication systems are described that use signal constellations, which have unequally spaced (i.e. ‘geometrically’ shaped) points. In many embodiments, the communication systems use specific geometric constellations that are capacity optimized at a specific SNR. In addition, ranges within which the constellation points of a capacity optimized constellation can be perturbed and are still likely to achieve a given percentage of the optimal capacity increase compared to a constellation that maximizes dmin, are also described. Capacity measures that are used in the selection of the location of constellation points include, but are not limited to, parallel decode (PD) capacity and joint capacity.