Protograph LDPC Rate Compatibility With Linear Minimum Distance

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Solution Overview

Problem

Existing methods for constructing low-density parity-check (LDPC) codes struggle to design rate-compatible families with the linear minimum distance property and low iterative decoding thresholds, particularly in achieving various code rates with fixed input or output block sizes while maintaining efficiency and error floor performance.

Innovation Solution

The method involves starting with a base protograph having variable node degrees of at least 3, applying operations such as splitting check nodes into two and connecting them with degree-2 variable nodes, and adjusting the status of these nodes to create protographs with identical structures for different rates, ensuring linear minimum distance and low iterative decoding thresholds.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If check nodes are split and connected with degree-2 variable nodes to create rate-compatible families, then code rate flexibility is improved, but graph structure complexity increases

Engineering Contradiction:

Improvecode rate flexibilityVSAvoidgraph structure complexity

Core Design Contradiction:

Adaptability or versatilityVSDevice complexity

Solution Approach 1:

The patent applies segmentation by splitting check nodes into multiple components and introducing degree-2 variable nodes as intermediate elements. This segmentation allows the base protograph to be transformed into multiple rate-compatible variants while maintaining a systematic structure that manages complexity through modular decomposition of the code construction process.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

Degree-2 variable nodes serve as intermediaries between check nodes in the protograph structure. These intermediary nodes enable rate compatibility by providing a standardized mechanism to adjust code rates without fundamentally redesigning the entire graph structure, thus managing complexity while achieving versatility.

Inventive Principle:

Principle #24Intermediary (Mediator)

2Reliability

If protographs are designed with variable node degrees of at least 3, then linear minimum distance property is improved, but ability to achieve low iterative decoding thresholds deteriorates

Engineering Contradiction:

Improvelinear minimum distance propertyVSAvoiditerative decoding threshold

Core Design Contradiction:

ReliabilityVSManufacturing precision

Solution Approach 1:

The patent applies local quality by allowing specific local deviations from the degree-3 constraint while maintaining the overall linear minimum distance property. Degree-2 variable nodes are introduced in controlled local configurations that preserve global reliability properties while locally enabling improved decoding thresholds through optimized connection patterns.

Inventive Principle:

Principle #3Local quality

3Productivity

If rate-compatible families are constructed with fixed input block size, then encoding efficiency is improved, but code rate adaptability deteriorates

Engineering Contradiction:

Improveencoding efficiencyVSAvoidcode rate adaptability

Core Design Contradiction:

ProductivityVSAdaptability or versatility

Solution Approach 1:

The patent applies dynamics by creating a systematic transformation mechanism where a single base protograph can dynamically generate multiple rate-compatible codes. The degree-2 variable nodes provide dynamic adjustment capability, allowing the same base structure to adapt to different code rates while maintaining fixed input block size for encoding efficiency.

Inventive Principle:

Principle #15Dynamics

4Productivity

If rate-compatible families are constructed with fixed output block size, then decoding efficiency is improved, but code rate adaptability deteriorates

Engineering Contradiction:

Improvedecoding efficiencyVSAvoidcode rate adaptability

Core Design Contradiction:

ProductivityVSAdaptability or versatility

Solution Approach 1:

The patent applies universality by designing a base protograph structure that serves multiple functions across different code rates. The systematic use of degree-2 variable nodes creates a universal template that can be instantiated at various rates while maintaining consistent output block sizes, enabling a single decoder design to handle multiple rates efficiently.

Inventive Principle:

Principle #6Universality (Multi-functionality)

Data Source

PatentUS8117523B2Rate-compatible protograph LDPC code families with linear minimum distance

Publication Date: 2012.02.14 CALIFORNIA INST OF TECH

AI summary

Digital communication coding methods are shown, which generate certain types of low-density parity-check (LDPC) codes built from protographs. A first method creates protographs having the linear minimum distance property and comprising at least one variable node with degree less than 3. A second method creates families of protographs of different rates, all having the linear minimum distance property, and structurally identical for all rates except for a rate-dependent designation of certain variable nodes as transmitted or non-transmitted. A third method creates families of protographs of different rates, all having the linear minimum distance property, and structurally identical for all rates except for a rate-dependent designation of the status of certain variable nodes as non-transmitted or set to zero. LDPC codes built from the protographs created by these methods can simultaneously have low error floors and low iterative decoding thresholds, and families of such codes of different rates can be decoded efficiently using a common decoding architecture.