LDPC Parity-Check Matrix Layout for Windowed Decoding Convergence

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Solution Overview

Problem

Existing LDPC code constructions face challenges in encoding difficulty, irregularity leading to non-optimum parallel decoding, and suboptimal convergence of decoding algorithms due to random parity check matrices and memory access conflicts.

Innovation Solution

A parity check matrix is constructed with a systematic matrix and a parity matrix, where rows are distributed in decoding windows of the same size, and elements in at least one column of the systematic matrix are '0's except for a single '1', allowing data variables to be involved in only one parity equation per decoding window, optimizing convergence and memory access.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If a random parity check matrix is used for LDPC codes, then decoding performance is improved, but encoding difficulty increases and parallel decoding becomes non-optimum

Engineering Contradiction:

Improvedecoding performanceVSAvoidencoding difficulty

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The parity check matrix is divided into sub-matrices with specific structures (circulant matrices for systematic part, identity matrices for parity part), allowing separate optimization of encoding and decoding functions while maintaining overall decoding performance

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

Different parts of the parity check matrix are assigned different properties: the systematic part uses structured circulant matrices for easy encoding, while the parity part uses identity matrices for optimal parallel decoding, achieving local optimization for each function

Inventive Principle:

Principle #3Local quality

2Ease of manufacture

If an irregular repeat-accumulate code construction is used, then encoding is simplified, but parallel decoding becomes non-optimum due to irregularity

Engineering Contradiction:

Improveencoding simplicityVSAvoidparallel decoding efficiency

Core Design Contradiction:

Ease of manufactureVSProductivity

Solution Approach 1:

The parity check matrix is constructed with homogeneous sub-matrices (circulant and identity matrices of fixed sizes) arranged in a regular pattern, enabling uniform parallel processing while maintaining encoding simplicity through the structured form

Inventive Principle:

Principle #33Homogeneity

3Productivity

If a regular quasi-cyclic form parity check matrix is used, then parallel decoding is improved, but encoding becomes difficult

Engineering Contradiction:

Improveparallel decoding efficiencyVSAvoidencoding difficulty

Core Design Contradiction:

ProductivityVSDevice complexity

Solution Approach 1:

The parity check matrix is segmented into distinct functional regions: a systematic part with circulant matrices optimized for encoding and a parity part with identity matrices optimized for parallel decoding, allowing each part to be optimized for its specific purpose

Inventive Principle:

Principle #1Segmentation

4Productivity

If multiple simultaneous memory accesses are implemented in parallel decoding, then decoding speed is improved, but memory access conflicts increase

Engineering Contradiction:

Improvedecoding speedVSAvoidmemory access efficiency

Core Design Contradiction:

ProductivityVSReliability

Solution Approach 1:

The parity check matrix is organized into decoding windows with a specific two-dimensional structure, allowing parallel processing operations to access memory in a conflict-free manner by distributing accesses across different memory locations through the structured matrix form

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

Data Source

PatentUS8271851B2Encoding and decoding a data signal as a function of a correcting code

Publication Date: 2012.09.18 3G LICENSING SA

AI summary

The invention relates to correcting codes for encoding and decoding a data signal. A signal including data variables is coded into a signal including the data variables and parity variables. The encoding and decoding operations are based on a parity check matrix comprised of a systematic matrix and a parity matrix and having rows corresponding coefficients of parity equations and distributed into decoding windows of same size. In order to increase convergence of the iterative decoding, the elements of at least one column of the systematic matrix associated with a decoding window are “0s”, except for a single element which is a “1”. A data variable is only involved in one equation of the window and not involved in solving the equations of other windows as long as the solving of equations of the window is not achieved.