Nearest-Neighbor LLR Decoding for High-Dimensional Modulation
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Solution Overview
Problem
The computational complexity of calculating log-likelihood ratios (LLRs) for modulated symbols in digital communication systems, particularly in optical communication systems using high-dimensional modulation formats, is high, necessitating a more efficient method to reduce complexity while maintaining accuracy.
Innovation Solution
The method involves approximating LLRs by considering only the most likely nearest neighbor codewords, using belief propagation over factor graphs, and refining outputs with nonlinear filters like artificial neural networks and Volterra filters, while pruning minor edges for reduced complexity and employing stochastic back-propagation for reinforcement learning to enhance accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If all codewords are considered for LLR calculation, then decoding accuracy is improved, but computational complexity increases significantly
Solution Approach 1:
The patent segments the constellation of codewords into multiple clusters, where each cluster contains a subset of codewords. Instead of evaluating all codewords, the system divides the search space into manageable segments and performs LLR calculations only within relevant clusters, significantly reducing computational complexity while maintaining accurate decoding performance
Solution Approach 2:
The patent applies partial action by considering only a subset of the most likely nearest neighbor codewords rather than all possible codewords. By identifying and evaluating only the most relevant codewords that have significant probability mass, the system achieves sufficient decoding accuracy without the excessive computational burden of exhaustive search
2Use of energy by moving object
If high-dimensional modulation formats are used, then power efficiency is improved, but LLR calculation complexity increases
Solution Approach 1:
The patent segments high-dimensional modulation constellations into multiple lower-dimensional clusters or groups. By organizing the high-dimensional signal space into structured segments, the system can perform LLR calculations on reduced subsets of codewords within each cluster, making high-dimensional modulation formats computationally tractable while preserving their power efficiency advantages
Solution Approach 2:
The patent transforms the high-dimensional LLR calculation problem into a series of lower-dimensional subproblems by projecting or mapping the high-dimensional constellation onto multiple lower-dimensional subspaces. This dimensionality reduction approach maintains the benefits of high-dimensional modulation while reducing the computational complexity of LLR calculations to manageable levels
Data Source
AI summary
A method receives the symbol transmitted over a channel, selects, from a constellation of codewords, a first codeword neighboring the received symbol and a set of second codewords neighboring the first codeword, and determines a relative likelihood of each second codeword being the transmitted symbol with respect to a likelihood of the first codeword being the transmitted symbol. Next, the method determines an approximation of a log-likelihood ratio (LLR) of each data bit in the received symbol as a log of a ratio of a sum of the relative likelihoods of at least some of the second codewords having the same value of the data bit to a sum of the relative likelihoods of at least some of the second codewords having different value of the data bit and decodes the received symbol using the LLR of each data bit.