Extended-Lattice MAP Decoding for Non-Uniform Symbol Signals
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Solution Overview
Problem
Current decoding methods for information symbols with non-uniform probability distributions, such as those encountered in network coding, are either overly complex like MAP decoding or sub-optimal like ML decoding, leading to high error rates and computational challenges.
Innovation Solution
A simplified MAP decoding method that models the sum symbol using a Gaussian distribution and employs an augmented network to find the nearest neighbor of the received signal, reducing the search space and using a sphere decoder or battery-powered decoder to efficiently estimate the received symbol.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If MAP decoding is used for non-uniform information sources, then decoding accuracy is improved, but computational complexity increases significantly
Solution Approach 1:
The patent segments the complex MAP decoding problem into two parts: (1) transforming the non-uniform probability distribution into a uniform one through a mapping function, and (2) applying simplified ML decoding on the transformed uniform distribution. This segmentation allows the system to achieve near-MAP accuracy with ML-level computational complexity.
Solution Approach 2:
The patent changes the parameter space by applying a mapping function that transforms symbols from a non-uniform probability distribution into a uniform probability distribution. This parameter transformation allows standard ML decoding algorithms to be applied effectively, resolving the contradiction between accuracy and complexity.
2Device complexity
If ML decoding is used for simplicity, then computational complexity is reduced, but decoding accuracy deteriorates for non-uniform information sources
Solution Approach 1:
Instead of applying complex MAP decoding directly to the original non-uniform distribution, the patent inverts the approach by first transforming the non-uniform distribution into a uniform one through a mapping function, then applying simple ML decoding. This inversion allows ML decoding to achieve accuracy comparable to MAP decoding.
3Measurement precision
If exhaustive search is performed for optimal decoding, then decoding accuracy is improved, but processing time increases significantly
Solution Approach 1:
The patent performs a preliminary action by pre-computing the mapping function that transforms the non-uniform probability distribution into a uniform one. This preliminary transformation allows subsequent decoding to be performed efficiently using simple ML decoding without requiring exhaustive search, thus reducing processing time while maintaining accuracy.
Data Source
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AI summary
The invention relates to a method for MAP decoding of a signal received through a noisy channel. The signal is made up of alphabet symbols having non-uniform probability distribution. The symbols are represented by points from a point array (Λ). The probability distribution of the symbols is approximated by a Gaussian distribution. An expanded point array (Λaug) is constructed from the point array (Λ) and the ratio (β) between the noise variance and the variance in Gaussian distribution of the symbols. The proposed MAP decoding method then goes back to carrying out decoding according to ML criteria by searching for the point, from the expanded array, that is nearest to a point representing the received signal (yaug).