QC-LDPC Parity Matrix Structure for Faster 5/6 Encoding
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Solution Overview
Problem
Existing LDPC codes face challenges with high computational intensity due to high-density generator matrices, limiting their practical application, especially in wireless communication systems, and there is a need for improved error correction codes with longer block lengths and efficient encoding/decoding processes.
Innovation Solution
The development of quasi-cyclic low-density parity-check (QC-LDPC) codes with a block length of 7776 and a code rate of 5/6, utilizing a parity check matrix with a quasi-cyclic structure and Khatri-Rao lifting to enhance encoding and decoding efficiency, allowing for parallel and concurrent processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If high-density generator matrices are used for LDPC coding, then error correction capability is improved, but computational complexity increases significantly
Solution Approach 1:
The generator matrix is segmented into multiple sub-matrices with a quasi-cyclic structure, where each sub-matrix corresponds to a specific pattern of non-zero elements. This segmentation allows the encoding process to be divided into multiple simpler operations, reducing the overall computational complexity while maintaining the error correction capability provided by the dense structure.
Solution Approach 2:
The patent changes the structural parameters of the generator matrix from a completely dense form to a quasi-cyclic form with specific patterns of non-zero elements. This parameter change maintains the high error correction capability while reducing computational complexity by exploiting the repetitive structure for efficient encoding operations.
2Reliability
If longer block lengths are used for LDPC codes, then error correction performance is improved, but encoding and decoding processing time increases
Solution Approach 1:
The long block length code is segmented into multiple shorter sub-blocks through the quasi-cyclic structure, where each sub-block can be processed independently or in parallel. This segmentation maintains the benefits of long block length for error correction while reducing the processing time by enabling parallel computation across sub-blocks.
Solution Approach 2:
The quasi-cyclic structure introduces periodicity in the generator matrix pattern, allowing the encoding and decoding processes to reuse the same computational operations at regular intervals. This periodic action reduces the overall processing time for long block lengths by avoiding redundant computations.
3Reliability
If complex encoding processes are used to generate parity bits, then error correction capability is improved, but processing efficiency decreases
Solution Approach 1:
The encoding process parameters are changed from general dense matrix multiplication to structured quasi-cyclic matrix operations with predefined patterns. This parameter change maintains the error correction capability while improving processing efficiency by reducing the number of required computational operations through the structured approach.
Solution Approach 2:
The quasi-cyclic structure allows the same sub-matrix patterns to be copied and reused multiple times throughout the generator matrix. This copying approach maintains the complex error correction capability while improving processing efficiency by avoiding redundant computation of identical sub-matrices.
Data Source
AI summary
An apparatus may include a transmitter and one or more processors. The one or more processors may be configured to identify, according to a code rate of 5/6 and a code block size of 7776 bits, a first binary parity check matrix for a quasi-cyclic-low-density parity-check (QC-LDPC) code, the first binary parity check matrix corresponding to a first exponent matrix. The one or more processors may be configured to encode data using the first binary parity check matrix. The transmitter may be configured to transmit the encoded data.