LDPC Parity-Check Matrix Structure for Low-Complexity Encoding

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Solution Overview

Problem

Existing LDPC code structures face challenges in maintaining error-correction capability due to columns with weight one, which degrade performance, and require complex computations for generator matrix evaluation, especially when parity-check matrices are not sparse or uniformly weighted.

Innovation Solution

A method and system for encoding and decoding using a parity-check matrix structured with sub-block matrices, where the parity portion has an upper diagonal defined by identity or permutation matrices, and columns below the diagonal are mostly zero matrices, allowing for efficient computation and improved error-correction capabilities.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Ease of manufacture

If a random sparse parity-check matrix is used, then the structure is simple to create, but the sparseness is lost after Gaussian elimination and the matrix may not have independent rows

Engineering Contradiction:

Improveease of creating parity-check matrixVSAvoiderror-correction capability

Core Design Contradiction:

Ease of manufactureVSReliability

Solution Approach 1:

The parity-check matrix is divided into two separate sparse matrices H1 and H2, where H1 corresponds to data bits and H2 corresponds to parity bits. This segmentation allows H to maintain sparseness while ensuring full rank, as H2 is specifically designed with a lower triangular structure that guarantees independence of rows.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

Different parts of the parity-check matrix are given different properties: H1 is designed to be sparse for efficiency, while H2 is designed with a lower triangular structure for computational ease. This local differentiation allows each part to serve its specific function optimally.

Inventive Principle:

Principle #3Local quality

2Device complexity

If H2 is constructed in lower triangular form, then the parity bits can be solved recursively without evaluating the generator matrix, but the encoding complexity increases

Engineering Contradiction:

Improveencoding complexityVSAvoidease of computing parity bits

Core Design Contradiction:

Device complexityVSEase of operation

Solution Approach 1:

The parity-check matrix is segmented into H1 and H2, where H2's lower triangular structure enables direct recursive computation of parity bits from data bits without requiring full generator matrix evaluation, thus reducing overall encoding complexity.

Inventive Principle:

Principle #1Segmentation

3Ease of manufacture

If columns with weight one are present in the parity-check matrix, then the matrix structure is simple, but the error-correction capability degrades

Engineering Contradiction:

Improveease of constructing matrixVSAvoiderror-correction performance

Core Design Contradiction:

Ease of manufactureVSReliability

Solution Approach 1:

Different column weight distributions are assigned to different parts of the matrix: H1 uses varied column weights optimized for error correction, while H2 uses a structured lower triangular form with controlled column weights, ensuring overall matrix performance.

Inventive Principle:

Principle #3Local quality

Data Source

PatentUS8196012B2Method and system for encoding and decoding low-density-parity-check (LDPC) codes

Publication Date: 2012.06.05 THE HONG KONG POLYTECHNIC UNIV

AI summary

An approximated lower-triangle structure for the parity-check matrix of low-density parity-check (LDPC) codes which allows linear-time-encoding complexity of the codes is disclosed, and the parity part of the parity-check matrix is semi-deterministic which allows high flexibility when designing the LDPC codes in order to provide higher error-correction capabilities than a typical dual-diagonal structure.