Shortened EG-LDPC Codes for Flexible Length and Rate Control

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Solution Overview

Problem

Low density parity check (LDPC) codes, particularly EG-LDPC codes, have limited flexibility in code lengths and rates due to their finite Euclidean geometries, which restricts their performance in various coding applications.

Innovation Solution

The method involves code shortening techniques that rearrange the columns of a parity check matrix into parallel classes, allowing for the removal of blocks to create new codes with adjusted rates and lengths without significantly reducing performance, thereby expanding the range of achievable code parameters.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If EG-LDPC codes are constructed using finite Euclidean geometries, then minimal distance is improved, but flexibility in code lengths and rates deteriorates

Engineering Contradiction:

Improveminimal distanceVSAvoidflexibility in code lengths and rates

Core Design Contradiction:

ReliabilityVSAdaptability or versatility

Solution Approach 1:

The code is segmented into a first set of information bits and a second set of information bits. The first set is encoded using the EG-LDPC code construction based on finite Euclidean geometry to ensure high minimal distance, while the second set is encoded using a different construction to provide flexibility in code lengths and rates. This segmentation allows each part to optimize for its specific function.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent employs a composite coding approach where two different LDPC code constructions are combined into a single code structure. The first construction (EG-LDPC) provides excellent error correction performance through high minimal distance, while the second construction provides adaptability in code parameters. This composite structure integrates the advantages of both approaches.

Inventive Principle:

Principle #40Composite materials

2Adaptability or versatility

If code shortening techniques are applied to EG-LDPC codes, then flexibility in code parameters is improved, but performance may deteriorate

Engineering Contradiction:

Improveflexibility in code parametersVSAvoidperformance

Core Design Contradiction:

Adaptability or versatilityVSReliability

Solution Approach 1:

The code is divided into two segments with different encoding approaches. The first segment uses EG-LDPC construction for high performance, while the second segment uses an alternative construction that facilitates code shortening and parameter adjustment. This segmentation enables flexibility without compromising the performance-critical first segment.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

Different parts of the code are assigned different quality characteristics. The first set of information bits (more critical for performance) is protected by the high-performance EG-LDPC construction, while the second set (more flexible) uses a construction that allows easier parameter adjustment. This local differentiation optimizes both performance and flexibility.

Inventive Principle:

Principle #3Local quality

Data Source

PatentUS7624334B2Construction and use of shortened EG-LDPC codes

Publication Date: 2009.11.24 APPLE INC

AI summary

Code shortening techniques are used to achieve a variety of code lengths and code rates for Euclidean geometry low density parity check (EG-LDPC) codes.