LDPC Encoding Loop Unrolling with Sparse Matrix Operations
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Low-density parity-check (LDPC) encoding processes, used in noisy communication channels, face inefficiencies due to large generator matrices that require extensive processing resources and time, making real-time communications challenging.
Innovation Solution
The use of a smaller matrix representation that specifies the location of non-zero entries in the LDPC encoding matrix, allowing for the generation of optimized operations for encoding, which reduces processing time and resource requirements through techniques like loop unrolling, constant propagation, and strength reduction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a large generator matrix is used for LDPC encoding, then encoding accuracy is improved, but processing time increases and real-time communication becomes difficult
Solution Approach 1:
The patent divides the large generator matrix into multiple smaller sub-matrices or blocks. By segmenting the encoding process into smaller units, the processing time is reduced while maintaining the overall encoding accuracy. This allows the encoding to be performed in parallel or sequentially on smaller data units, improving real-time performance.
Solution Approach 2:
The patent performs preliminary processing on the generator matrix by pre-computing and storing certain encoding parameters, lookup tables, or transformed representations of the matrix. This preliminary action enables faster encoding operations during actual communication by avoiding redundant computations, thus reducing processing time while preserving encoding accuracy.
2Reliability
If a large generator matrix is used for LDPC encoding, then encoding accuracy is improved, but hardware resource requirements and circuitry area increase
Solution Approach 1:
The patent segments the large generator matrix into smaller sub-matrices, which can be implemented as separate modular encoding units in hardware. This segmentation reduces the area required for each individual encoding unit, allowing the overall system to fit within available hardware resources while maintaining encoding accuracy through the combined operation of multiple smaller units.
Solution Approach 2:
The patent uses compressed or simplified representations of the generator matrix, such as storing only non-zero elements, sparse matrix formats, or pre-computed encoding parameters. This copying approach reduces the hardware resources needed to store and process the matrix while maintaining the same encoding functionality and accuracy.
3Ease of operation
If nested FOR loops are used to implement matrix multiplication, then encoding functionality is achieved, but execution speed on processors becomes slow
Solution Approach 1:
The patent performs loop unrolling and pre-computation of matrix multiplication operations. By unrolling the nested loops and pre-calculating certain terms, the patent eliminates the overhead of loop control and reduces the number of iterative operations, thereby significantly improving execution speed while maintaining the correct encoding functionality.
Solution Approach 2:
The patent changes the computational parameters by transforming the matrix multiplication into alternative mathematical forms, such as using fast Fourier transform (FFT)-based multiplication, exploiting the sparse structure of the generator matrix, or applying algebraic simplifications. These parameter changes reduce the computational complexity and improve execution speed while preserving encoding accuracy.
Data Source
AI summary
Techniques are disclosed relating to encoding communications. In some embodiments, for different rows of an encoding matrix, the following operations are performed: generate a set of operations for entries in the row, where the set of operations includes respective operations to be performed on the entries for multiplication of the matrix by a vector, propagate values of entries in the encoding matrix into the set of operations, and simplify ones of the set of operations based on the propagated values to generate an output set of operations. In some embodiments, the output sets of operations are usable to encode input data for communication over a medium. In some embodiments, the disclosed techniques facilitate loop unrolling within compiler memory constraints. In some embodiments, an apparatus (e.g., a mobile device) is configured with the output sets of operations.