Rate-Compatible LDPC Matrices With Constant Blocklength
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Solution Overview
Problem
Existing low-density parity-check (LDPC) codes face performance degradation when transitioning between different transmission rates due to techniques like puncturing and shortening, which reduce code blocklength and degrade performance significantly for higher and lower-rate codes.
Innovation Solution
Generating higher-rate LDPC matrices by combining rows of a lower-rate 'mother' LDPC matrix with the same code blocklength, maintaining identical blocklength and variable degree distribution across different code rates, and employing specific structural constraints for reduced encoder complexity and decoder latency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If puncturing is used to generate higher-rate codes, then code rate is improved, but code blocklength is reduced which degrades performance
Solution Approach 1:
The patent combines multiple rows of the lower-rate LDPC matrix to form rows of the higher-rate LDPC matrix. Specifically, each row in the higher-rate matrix is formed by combining (XOR operation) a selected subset of rows from the lower-rate matrix, allowing the higher-rate code to maintain the same blocklength while achieving the desired code rate through selective row combination and puncturing of parity bits.
Solution Approach 2:
The patent creates a universal LDPC matrix structure that can serve multiple code rates. By organizing the LDPC matrix such that higher-rate codes are derived from lower-rate codes through systematic row combining and puncturing, a single base matrix structure supports multiple transmission rates without requiring separate code designs for each rate, thus achieving multi-functionality.
2Productivity
If shortening is used to generate lower-rate codes, then code rate is reduced, but code blocklength is reduced which degrades performance
Solution Approach 1:
The patent combines multiple rows of the lower-rate LDPC matrix to form rows of the higher-rate LDPC matrix. Specifically, each row in the higher-rate matrix is formed by combining (XOR operation) a selected subset of rows from the lower-rate matrix, allowing the higher-rate code to maintain the same blocklength while achieving the desired code rate through selective row combination and puncturing of parity bits.
Solution Approach 2:
The patent creates a universal LDPC matrix structure that can serve multiple code rates. By organizing the LDPC matrix such that higher-rate codes are derived from lower-rate codes through systematic row combining and puncturing, a single base matrix structure supports multiple transmission rates without requiring separate code designs for each rate, thus achieving multi-functionality.
3Adaptability or versatility
If different LDPC matrices are used for different rates, then code rate adaptability is improved, but device complexity increases
Solution Approach 1:
The patent creates a universal LDPC matrix structure that can serve multiple code rates. By organizing the LDPC matrix such that higher-rate codes are derived from lower-rate codes through systematic row combining and puncturing, a single base matrix structure supports multiple transmission rates without requiring separate code designs for each rate, thus achieving multi-functionality.
Solution Approach 2:
The patent enables dynamic rate adaptation by allowing the system to selectively use different rows from the LDPC matrix based on the desired code rate. The encoder can dynamically adjust which parity bits are transmitted and which are punctured, while the decoder can dynamically adjust its processing based on the received rate, providing flexible rate compatibility without hardware reconfiguration.
Data Source
AI summary
Low density parity check (LDPC) codes (LDPCCs) have an identical code blocklength and different code rates. At least one of the rows of a higher-rate LDPC matrix is obtained by combining a plurality of rows of a lower-rate LDPC matrix with the identical code blocklength as the higher-rate LDPC matrix.