LDPC Parity Check Matrix Compression for Generic FEC Decoding
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Solution Overview
Problem
Existing methods for signaling parity check matrices in forward error correction (FEC) schemes are inefficient, leading to complex computations and high data requirements, especially in multicast transmissions where the receiving end must reconstruct large matrices from sparse binary LDPC codes.
Innovation Solution
A method for compressing binary parity check matrices using run-length encoding or selecting row and column indices, allowing for efficient transmission and reconstruction at the receiving end without prior knowledge of the encoding scheme, thereby reducing computational complexity and data volume.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the complete binary parity check matrix is transmitted to the receiving end, then the receiving end can accurately reconstruct the decoding graph for message-passing decoding, but the data transmission volume becomes very large (typically a few millions of elements)
Solution Approach 1:
The patent extracts only the essential elements needed for decoding - specifically the column indices of 'ones' in the parity check matrix organized by row - rather than transmitting the complete matrix. This extraction approach reduces the transmitted data from millions of elements to a compact representation that enables reconstruction at the receiving end.
Solution Approach 2:
The patent changes the representation parameters of the parity check matrix from a dense binary matrix format to a sparse coordinate format (row indices and column indices of non-zero elements). This parameter transformation dramatically reduces the data volume while preserving all necessary information for decoding graph construction.
2Reliability
If the receiving end uses a specific decoder that understands the KEY and encoding scheme, then the decoding performance can be optimized, but the device complexity and computational requirements increase
Solution Approach 1:
The patent creates a universal decoding graph construction method that can be implemented by any generic decoder without requiring knowledge of the specific encoding scheme or KEY. The receiving end uses the transmitted row and column indices to universally construct the decoding graph, making the solution applicable to various decoder implementations while maintaining optimal decoding performance.
Solution Approach 2:
The receiving end autonomously reconstructs the decoding graph using the transmitted index information without requiring external assistance or pre-programmed knowledge of the encoding scheme. The generic decoder self-configures by building the decoding graph from the received row and column indices, eliminating the need for complex pre-configured decoders.
3Quantity of substance
If run-length encoding is used to compress the binary parity check matrix, then the data amount for signaling is significantly reduced, but the compression algorithm adds processing steps at the transmitting end
Solution Approach 1:
The patent extracts only the column indices of non-zero elements (ones) from the binary parity check matrix, organized by their row positions. This extraction eliminates the need for complex compression algorithms while achieving significant data reduction, as only the essential variable information (column indices) is transmitted rather than the complete matrix structure.
Data Source
AI summary
To support a forward error correction scheme, in which a code of the forward error correction scheme is employed at a transmitting end for encoding data for a transmission to a receiving end, the transmitting end compresses at least one binary parity check matrix associated to the employed code of the forward error correction scheme. The transmitting end then provides the compressed binary parity check matrix for a transmission to the receiving end. The receiving end receives the compressed binary parity check matrix and decompresses it for use in a forward error correction based on encoded data received from the transmitting end.