Partitioned Distribution Matching for Low-Latency Probabilistic Shaping
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Solution Overview
Problem
Current methods for mapping sequences of uniformly distributed bits to non-equiprobable symbols in digital communications systems, such as constant composition distribution matching, suffer from high complexity and latency due to the need for long sequences and sequential decoding algorithms, which limit their efficiency in achieving low rate loss.
Innovation Solution
The approach involves partitioning a set of symbols into unique subsets with different permutations, allowing for a block-by-block transformation to achieve a desired non-uniform distribution, reducing the length of the block to be transformed and enabling a combination of distribution matchers with different probability mass functions to achieve a target distribution, thereby reducing rate loss and increasing transmission rate.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If constant composition distribution matching is used to map equiprobable bits to non-equiprobable symbols, then the desired non-uniform distribution is achieved, but very long sequences are required which causes high complexity and latency
Solution Approach 1:
The patent divides the long sequence into multiple blocks, where each block is transformed independently using distribution matchers. This segmentation allows achieving the desired distribution without requiring very long sequences, thereby reducing complexity and latency while maintaining distribution accuracy.
Solution Approach 2:
The patent uses multiple distribution matchers with different probability mass functions that can be dynamically selected and combined. By varying the PMFs across blocks and using probabilistic combination, the system achieves the target distribution with shorter block lengths compared to traditional constant composition methods.
2Manufacturing precision
If sequential decoding algorithms are used for distribution matching, then the desired symbol probability mass function is achieved, but prohibitively high complexity and latency result
Solution Approach 1:
The patent segments the sequential decoding process into independent block-wise operations. Each block can be processed separately using parallel distribution matchers, eliminating the need for sequential processing across the entire sequence. This dramatically reduces decoding complexity and latency while maintaining PMF accuracy.
Solution Approach 2:
The patent combines multiple distribution matchers with different PMFs in parallel, where each matcher handles a portion of the transformation. The combined output of these parallel matchers achieves the target distribution without requiring sequential processing, thereby reducing overall system complexity.
3Loss of energy
If constant composition distribution matching is used to achieve low rate loss, then arbitrarily low rate loss is achieved for asymptotically long sequences, but the method requires very long sequences which increases latency
Solution Approach 1:
The patent divides the transformation into independent blocks that can be processed in parallel. This segmentation enables achieving low rate loss with finite, relatively short block lengths rather than requiring asymptotically long sequences, thereby significantly reducing latency while maintaining efficiency.
Solution Approach 2:
The patent changes the parameter of block length from asymptotically long to finite and relatively short by using multiple distribution matchers with different PMFs. This parameter change allows achieving low rate loss without the latency penalty of very long sequences.
Data Source
AI summary
A communication system includes a data source to receive a block of bits, a memory to store a set of distribution matchers. Each distribution matcher is associated with a probability mass function (PMF) to match equally likely input bits to a fixed number of output bits with values distributed according to the PMF of the distribution matcher. Each distribution matcher is associated with a selection probability, such that a sum of joint probabilities of all distribution matchers equals a target PMF. A joint probability of a distribution matcher is a product of PMF of the distribution matcher with the selection probability of the distribution matcher. The communication system also includes a shaping mapper to select the distribution matcher from the set of distribution matchers with the selection probability and to map the block of bits to a block of shaped bits with a non-uniform distribution using the selected distribution matcher and a transmitter front end to transmit the block of shaped bits over a communication channel, such that bits in a sequence of the blocks of shaped bits are distributed according to the target PMF.