individual
What campus are you from?
Daytona Beach
Authors' Class Standing
Oshani Jayawardane, Graduate Student
Lead Presenter's Name
Oshani Jayawardane
Faculty Mentor Name
Dr. Sirani Perera
Abstract
Code Recovery using algebraic-geometric approaches becomes computationally expensive with the cardinality of the field and complex code structures. In response, we propose a low-complexity algorithm that utilizes structures in algebraic-geometric codes over finite fields. The low-complexity algorithm to locally recover algebraic codes over finite fields (i.e., πππ algorithm) is defined based on a sparse matrix factorization that computes the inverse of an (r+1) x r generator matrix, whose elements are defined by the points on the surface in PΒ³ over the finite field π½q with locality r. We have shown that the (πππ algorithm) reduces the complexity from O(nΒ³) to O(nlogn) for the n = 2Λ’ (s β₯ 1)> r length codeword. The extended πππ algorithm is proposed to globally recover codes over finite fields. As a benchmark, we design structured neural networks (StNNs), i.e., DFT-StNN and DCT-StNN, based on the factorization of the generator matrix to globally recover codes. Numerical Simulations were conducted to compare the performance of the extended πππ algorithm in global recovery codes, with brute-force calculation, DFT-StNN, DCT-StNN, and a feedforward neural network for codewords with lengths from n=6, 12, 27, 48, 96, and 210, having locality 2 for points on the surface PΒ³ over the finite field π½q. Our empirical results demonstrate that the extended πππ algorithm achieves the lowest flops, the highest accuracy with an error order 10β»ΒΉβΆ for all length codewords, compared to brute-force calculations, DFT-StNN, DCT-StNN, and the feedforward neural network.
Did this research project receive funding support from the Office of Undergraduate Research.
No
A Low-complexity Generator Matrix-influenced Algorithm to Globally Recover Algebraic Codes Over Finite Fields
Code Recovery using algebraic-geometric approaches becomes computationally expensive with the cardinality of the field and complex code structures. In response, we propose a low-complexity algorithm that utilizes structures in algebraic-geometric codes over finite fields. The low-complexity algorithm to locally recover algebraic codes over finite fields (i.e., πππ algorithm) is defined based on a sparse matrix factorization that computes the inverse of an (r+1) x r generator matrix, whose elements are defined by the points on the surface in PΒ³ over the finite field π½q with locality r. We have shown that the (πππ algorithm) reduces the complexity from O(nΒ³) to O(nlogn) for the n = 2Λ’ (s β₯ 1)> r length codeword. The extended πππ algorithm is proposed to globally recover codes over finite fields. As a benchmark, we design structured neural networks (StNNs), i.e., DFT-StNN and DCT-StNN, based on the factorization of the generator matrix to globally recover codes. Numerical Simulations were conducted to compare the performance of the extended πππ algorithm in global recovery codes, with brute-force calculation, DFT-StNN, DCT-StNN, and a feedforward neural network for codewords with lengths from n=6, 12, 27, 48, 96, and 210, having locality 2 for points on the surface PΒ³ over the finite field π½q. Our empirical results demonstrate that the extended πππ algorithm achieves the lowest flops, the highest accuracy with an error order 10β»ΒΉβΆ for all length codewords, compared to brute-force calculations, DFT-StNN, DCT-StNN, and the feedforward neural network.