LDPC Parity Check Matrix Lifting for Variable Packet Sizes
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Solution Overview
Problem
Existing LDPC codes struggle to efficiently encode and decode packets of varying sizes due to their design for specific packet sizes, limiting their adaptability and performance in communication systems.
Innovation Solution
The use of a set of base parity check matrices of different dimensions and lifting values of different powers of two allows for efficient LDPC encoding and decoding of packets of varying sizes, with the lifting process enabling parallel encoding and decoding and reducing description complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If an LDPC code is designed for a particular packet size, then encoding and decoding performance is optimized for that size, but the code cannot readily accommodate packets of varying sizes
Solution Approach 1:
The LDPC code is segmented into a base matrix and multiple lifting operations. The base matrix contains the fundamental code structure, while lifting operations with different values (L=1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024) allow the same base matrix to be expanded to support various packet sizes. This segmentation enables the code to maintain optimized performance for specific sizes while adapting to variable sizes.
Solution Approach 2:
The invention changes the parameter L (lifting value) to adapt the LDPC code to different packet sizes. By varying L among powers of two from 1 to 1024, the code structure scales accordingly, allowing the same base matrix to serve multiple packet size requirements while maintaining encoding and decoding performance through parameter adjustment rather than redesign.
2Reliability
If multiple LDPC codes are designed for different packet sizes, then each packet size can be optimally encoded, but the system complexity and number of matrices to manage increases
Solution Approach 1:
A single base parity check matrix is designed to serve multiple functions by supporting various lifting values. This universal base matrix can encode packets of different sizes (from 24 to 11264 bits) by applying different lifting operations, eliminating the need to design and manage multiple separate LDPC codes for different packet sizes while maintaining optimal encoding performance for each size category.
3Adaptability or versatility
If a large number of base parity check matrices are used to support varying packet sizes, then all packet sizes can be accommodated, but the description complexity and storage requirements increase
Solution Approach 1:
Instead of creating multiple base matrices to cover different packet sizes, the invention inverts the approach by creating one base matrix and using lifting operations to expand it. This inversion reduces description complexity because the base matrix is small and simple, while the variability in packet size support is achieved through the lifting parameter L rather than through complex matrix structures.
Data Source
AI summary
Techniques to support low density parity check (LDPC) encoding and decoding are described. In an aspect, LDPC encoding and decoding of packets of varying sizes may be supported with a set of base parity check matrices of different dimensions and a set of lifting values of different powers of two. A base parity check matrix G of dimension mB×nB may be used to encode a packet of kB=nB−mB information bits to obtain a codeword of nB code bits. This base parity check matrix may be “lifted” by a lifting value of L to obtain a lifted parity check matrix H of dimension L·mB×L·nB. The lifted parity check matrix may be used to encode a packet of up to L·kB information bits to obtain a codeword of L·nB code bits. A wide range of packet sizes may be supported with the set of base parity check matrices and the set of lifting values.