Geometrically Shaped Constellations for Higher Channel Capacity
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Solution Overview
Problem
Existing digital communication systems face limitations in achieving maximum capacity due to the use of constellations that are not optimized for signal-to-noise ratios, resulting in a significant gap from the theoretical Shannon Gaussian capacity, which restricts coding gains and efficiency in data transmission.
Innovation Solution
The development of geometrically shaped constellations that optimize capacity by selecting point locations in a one or multi-dimensional space to maximize transmission efficiency, allowing systems to transmit data at a lower power for a given rate or higher rate for the same power, without requiring specially designed coding mechanisms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional equally spaced constellations are used, then the system is simple to implement, but the capacity is significantly below the Shannon Gaussian capacity limit
Solution Approach 1:
The patent applies local quality by creating unequally spaced constellation points where different regions of the constellation have different spacing properties. Central points are spaced differently from edge points, optimizing the probability density distribution to better approximate a Gaussian distribution and thereby increase capacity without requiring complex coding mechanisms.
Solution Approach 2:
The patent changes the spatial parameters of the constellation by optimizing point locations based on probability density functions. By adjusting the spacing and distribution parameters of constellation points rather than using uniform spacing, the system achieves higher capacity closer to the Shannon limit while maintaining practical implementation feasibility.
2Productivity
If coding mechanisms are added to increase capacity, then the capacity approaches the Shannon limit, but the device complexity increases significantly
Solution Approach 1:
The patent extracts the capacity enhancement function from complex coding mechanisms and transfers it to the constellation design itself. By optimizing the constellation geometry and point distribution, the system achieves capacity improvements that were previously only attainable through sophisticated coding schemes, thereby reducing overall system complexity.
Solution Approach 2:
The patent substitutes the mechanical coding system with a geometric constellation optimization approach. Instead of using complex error correction codes to achieve capacity near the Shannon limit, the system uses optimized unequally spaced constellations that inherently provide higher capacity without requiring additional coding layers.
3Reliability
If the dimensionality of constellation is increased, then the minimum distance increases for constant energy, but the capacity is still limited by minimum distance criteria
Solution Approach 1:
The patent extends constellation design from two-dimensional QAM to three-dimensional and higher-dimensional constellations. By utilizing additional spatial dimensions, the system achieves better minimum distance properties for constant energy while simultaneously optimizing point distribution to maximize capacity, overcoming the limitations of traditional 2D constellations.
Solution Approach 2:
The patent applies local quality optimization in higher-dimensional space by creating unequally spaced point distributions that optimize both minimum distance and capacity simultaneously. Different regions of the high-dimensional constellation have optimized spacing to maximize the probability density approximation, achieving better performance than uniform spacing in any dimension.
Data Source
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AI summary
Communication systems are described that use geometrically shaped constellations that have increased capacity compared to conventional constellations operating within a similar SNR band. In several embodiments, the geometrically shaped is optimized based upon a capacity measure such as parallel decoding capacity or joint capacity. In many embodiments, a capacity optimized geometrically shaped constellation can be used to replace a conventional constellation as part of a firmware upgrade to transmitters and receivers within a communication system. In a number of embodiments, the geometrically shaped constellation is optimized for an Additive White Gaussian Noise channel or a fading channel. In numerous embodiments, the communication uses adaptive rate encoding and the location of points within the geometrically shaped constellation changes as the code rate changes. One embodiment of the invention includes a transmitter configured to transmit signals to a receiver via a communication channel, wherein the transmitter, includes a coder configured to receive user bits and output encoded bits at an expanded output encoded bit rate, a mapper configured to map encoded bits to symbols in a symbol constellation, a modulator configured to generate a signal for transmission via the communication channel using symbols generated by the mapper. In addition, the receiver includes a demodulator configured to demodulate the received signal via the communication channel, a demapper configured to estimate likelihoods from the demodulated signal, a decoder that is configured to estimate decoded bits from the likelihoods generated by the demapper. Furthermore, the symbol constellation is a capacity optimized geometrically spaced symbol constellation that provides a given capacity at a reduced signal-to-noise ratio compared to a signal constellation that maximizes dmin.