LDPC Parity Check Matrix for Error Detection in Short Blocks
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Solution Overview
Problem
In mobile communication systems, existing Low Density Parity Check (LDPC) codes face challenges in maintaining error detection capability while preserving error correction capability, especially in short-block lengths, which are essential for high-speed and high-capacity wireless data transmission.
Innovation Solution
The proposed solution involves generating a parity check matrix for LDPC codes by selecting and adding dependent parity check expressions to the original parity check matrix, optimizing the minimum distance and coding rate to enhance error correction and detection capabilities without reducing the coding rate.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If dependent parity check expressions are added to the parity check matrix to enhance error detection capability, then error detection capability is improved, but device complexity increases
Solution Approach 1:
The parity check matrix is segmented into a first parity check matrix for error correction and a second parity check matrix for error detection. This segmentation allows the system to maintain maximum error correction capability while adding error detection functionality through the structured inclusion of dependent parity check expressions in the second matrix.
Solution Approach 2:
The second parity check matrix serves multiple functions: it provides error detection capability while maintaining compatibility with the first parity check matrix for error correction. The dependent parity check expressions are designed to work together with the original parity check expressions, enabling a single LDPC code structure to achieve both error correction and error detection.
2Reliability
If the minimum distance is optimized to maintain error correction capability, then error correction capability is preserved, but the ability to add error detection expressions is limited
Solution Approach 1:
The solution adds a new dimension to the parity check matrix structure by introducing a second parity check matrix that operates in addition to the first. This dimensional expansion allows error detection functionality to be added without compromising the error correction capabilities established by the first matrix, as the two matrices operate in complementary dimensions.
Solution Approach 2:
The first parity check matrix is designed and optimized for error correction before the second matrix is introduced. By establishing the error correction foundation first and then adding error detection capabilities through the second matrix, the system preserves maximum error correction capability while gaining enhanced versatility.
Data Source
AI summary
An apparatus and method for decoding a Low Density Parity Check (LDPC) code having a maximum error correction capability and an error detection capability. In the apparatus, a decoder receives a signal, and decodes the received signal according to a second parity check matrix having parity check expressions obtained by selecting a predetermined number of dependent parity check expressions among dependent parity check expressions generated by combining, with a predetermined scheme, parity check expressions representing rows of a first parity check matrix obtained by encoding information data into a block code having an optimum minimum distance considering a predetermined coding rate, and adding the selected dependent parity check expressions to the parity check expressions of the first parity check matrix. An error detector determines if there is an error in a signal output from the decoder.