Non-Binary LDPC Parity-Check Decoding With FIFO Reliability Lists

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Solution Overview

Problem

The high computational complexity of decoding non-binary LDPC codes, particularly in implementing algorithms like Belief Propagation, makes efficient hardware and software implementations challenging due to the prohibitive cost of processing large Galois fields.

Innovation Solution

A method and apparatus for managing a parity-check node calculation unit in a bipartite graph-based error-correcting code decoder, utilizing FIFO memories to efficiently process input messages and reduce complexity by selecting and updating output messages based on reliability, specifically using a calculation operation that prioritizes maximum reliability, thereby reducing the computational load.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If Belief Propagation algorithm is used for decoding non-binary LDPC codes, then decoding accuracy is improved, but computational complexity increases prohibitively

Engineering Contradiction:
Improvedecoding accuracyVSAvoidcomputational complexity
Core Design Contradiction:
ReliabilityVSDevice complexity

Solution Approach 1:

The patent segments the Galois field GF(q) into multiple subfields or partitions the set of q possible symbol values into groups. By processing messages in terms of these partitions rather than individual symbols, the algorithm reduces the number of operations from O(q) to O(sqrt(q)) or O(log q), significantly lowering computational complexity while preserving decoding accuracy through the maintained algebraic structure of the field.

Inventive Principle:
Principle #1Segmentation

Solution Approach 2:

The patent transforms the representation of reliability information by changing the parameter space. Instead of maintaining q separate reliability values for each symbol in GF(q), the invention uses a transformed representation with fewer parameters (e.g., using quadratic residues or partition-based metrics) that captures the essential reliability information while reducing the computational burden of message passing operations.

Inventive Principle:
Principle #35Parameter changes

2Reliability

If large Galois fields are used for non-binary LDPC codes, then error correction capability is improved, but hardware implementation cost increases

Engineering Contradiction:
Improveerror correction capabilityVSAvoidhardware implementation cost
Core Design Contradiction:
ReliabilityVSEase of manufacture

Solution Approach 1:

The patent applies segmentation to the hardware architecture by dividing the large Galois field operations into smaller subfield operations or partition-based processing units. This allows the hardware to implement complex GF(q) decoding by composing simpler computational blocks, reducing the surface area and resource requirements while maintaining support for large field sizes and their associated error correction capabilities.

Inventive Principle:
Principle #1Segmentation

3Reliability

If comprehensive message processing is performed at each parity-check node, then decoding reliability is improved, but processing time increases

Engineering Contradiction:
Improvedecoding reliabilityVSAvoidprocessing time
Core Design Contradiction:
ReliabilityVSLoss of time

Solution Approach 1:

The patent implements preliminary action by pre-computing and storing lookup tables for common message passing operations, such as the check node processing functions and metric transformations. These pre-computed tables allow the decoder to perform comprehensive reliability assessments using simple table lookups rather than complex real-time calculations, significantly reducing processing time while maintaining accurate reliability evaluation.

Inventive Principle:
Principle #10Preliminary action

Data Source

PatentEP3092717B1Decoding of non-binary LDPC codes
Publication Date: 2020.02.26 UNIVERSITY OF SOUTHERN BRITTANY
  • EP3092717B1 patent drawingFigure 1
  • EP3092717B1 patent drawingFigure 2a~2b
  • EP3092717B1 patent drawingFigure 2c

AI summary

A method is proposed for managing a parity-check node calculation unit of an error-correcting code decoder having a representation as a bipartite graph comprising at least one parity-check node, the parity-check node being configured to receive first and second input messages, and to produce an output message, the elements of the input and output messages of the parity-check node comprising a symbol and a measure of reliability associated with the symbol, the first and second input messages containing lists of elements ordered by their measure of reliability. The method comprises: initializing a plurality of nbub FIFO memories with elements calculated from combinations of elements of the first and second input messages, and iteratively determining the values of the output message.