Irregular Block-Cyclic LDPC Codes With Low-Complexity Encoding
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Solution Overview
Problem
Existing Low-Density Parity-Check (LDPC) codes with regular row and column weights have limitations in error correction capability and encoding complexity, particularly in two-way communications systems like TWACS, which require improved performance and reduced implementation costs.
Innovation Solution
A family of LDPC codes with pseudo-random structure and low encoding complexity, allowing for irregular column and row weights, achieved through shortened, overlapping, or permuted blocks in the parity-check matrix, extending block-cyclic codes to enhance error correction and reduce implementation complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If random constructions are used for parity-check matrices, then error correction performance is improved, but encoding complexity increases
Solution Approach 1:
The parity-check matrix is divided into block-cyclic structures where each block has a regular pattern, allowing the encoder to process segments independently using simple shift-register operations rather than requiring full random matrix processing
Solution Approach 2:
Different blocks within the parity-check matrix have different cyclic shift amounts, creating local variations that provide randomness benefits while maintaining global structural regularity for simple encoding
2Device complexity
If regular row and column weight is used in parity-check matrices, then encoding complexity is reduced, but error correction capability deteriorates
Solution Approach 1:
The patent implements irregular row and column weights by assigning different cyclic shift amounts to different blocks, creating local variations in weight distribution that improve error correction while preserving the overall block-cyclic structure for simple encoding
Solution Approach 2:
The cyclic shift amounts are varied as parameters across different blocks, transforming the uniform regular structure into an irregular structure that provides better error correction performance while maintaining the block-cyclic encoding simplicity
3Reliability
If block-cyclic codes with irregular column weight are used, then error correction performance is improved, but the range of allowable weight distribution is limited
Solution Approach 1:
By allowing different blocks to have different cyclic shift amounts and different dimensions, the patent creates local variations that can be independently tuned to achieve a broader range of weight distributions compared to uniform block-cyclic codes
Solution Approach 2:
The block structure allows dynamic adjustment of cyclic shift amounts and block dimensions to adapt to different weight distribution requirements, providing versatility while maintaining the benefits of block-cyclic encoding
Data Source
AI summary
A set of irregular LDPC (Low Density Parity Check) codes having a pseudo-random structure and low encoding complexity. A block-cyclic LDPC code has an irregular row or an irregular column weight and includes a parity check matrix and an encoding matrix each of which has a pseudo-random structure. This allows the code to have the irregular row weight or irregular column weight together with an overall randomness to the code structure. Blocks within the code can be shortened, adjacent blocks of code can be overlapped, and adjacent columns within a block can be arbitrarily permuted so to change the weighting of rows and columns. The LDPC codes are particularly useful in two-way communications system for an electrical distribution system (1) to restore data lost or corrupted during its transmission.