LDPC Parity Check Matrix for Flexible Multi-Code-Rate Decoding
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Solution Overview
Problem
Conventional LDPC-based communication systems face inflexibility and complexity due to the need for redesigning check matrices and circuits when code rates change, leading to increased costs and reduced performance if punctured positions do not match the special check matrix.
Innovation Solution
A data decoding and transmitting method that adjusts the parity check matrix to match different code rates by using a parity check matrix of size (m1+m2)×(n1+n2) bits, incorporating local and global matrices, and employing a puncture method to determine the ratio of n2 and adjust the code rate, allowing for multi-code rate design.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a conventional check matrix is designed to match a special circuit and application environment, then the error correction performance is improved, but the system becomes inflexible when code rates change and requires redesigning the check matrix and circuit
Solution Approach 1:
The check matrix is divided into two parts: a first check matrix corresponding to transmitted bits and a second check matrix corresponding to untransmitted (punctured) bits. This segmentation allows the system to handle different code rates by selectively using portions of the overall check matrix structure, maintaining error correction performance while adapting to varying transmission requirements.
Solution Approach 2:
A single unified check matrix structure is designed to serve multiple code rates simultaneously. The check matrix is constructed with dimensions (m1+m2)×(n1+n2) where the first m1 rows correspond to transmitted bits and the second m2 rows correspond to punctured bits. This universal structure eliminates the need to redesign check matrices for different code rates, providing both reliability and adaptability.
2Productivity
If different puncture rates are applied to increase code rate, then the code rate is increased, but the performance is reduced if the punctured positions do not match the special check matrix
Solution Approach 1:
The check matrix is pre-configured with designated punctured positions during the matrix construction phase. The second check matrix corresponding to punctured bits is prepared in advance with appropriate column weights and structures. This preliminary arrangement ensures that when puncturing is applied to increase code rate, the punctured positions already match the optimized structure, maintaining error correction performance while achieving higher code rates.
3Productivity
If the code rate is increased from 0.50 to 0.51, then the code rate is increased by 0.01, but the Shannon limit varies by 0.043 dB
Solution Approach 1:
Different parts of the check matrix are assigned different column weight characteristics optimized for their specific functions. The first check matrix has column weights optimized for transmitted bits, while the second check matrix has column weights optimized for punctured bits. This local optimization allows the system to maintain better error correction performance when increasing code rate through puncturing, reducing the performance loss in terms of Shannon limit.
Data Source
AI summary
A data transmitting method using an LDPC code as an error correction code is provided. The method includes providing a parity check matrix of LDPC code, wherein the size of the parity check matrix is (m1+m2)×(n1+n2); in a sending side, encoding an input data of K bits with a encoder to generate a first block code of (n1+n2) bits, according to the parity check matrix; through a transmitting channel, sending n1 bits of the first block code from the sending side to a receiving side, wherein n2 bits of the first block code are not transmitted; and receiving the n1 bits of the first block code in the receiving side, and using the parity check matrix to perform a decoding algorithm to the received first block code to iterative decodes a second block code of (n1+n2) bits with a decoder. Furthermore, a data decoding method thereof is also provided.