Proceedings ArticleDOI
Exploring connections between Sparse Fourier Transform computation and decoding of product codes
Nagaraj Thenkarai Janakiraman,Santosh Kumar Emmadi,Krishna R. Narayanan,Kannan Ramchandran +3 more
- pp 1366-1373
TLDR
It is shown that the recently proposed Fast Fourier Aliasing-based Sparse Transform (FFAST) algorithm for computing the Discrete Fourier Transform (DFT) of signals with a sparse DFT is equivalent to iterative hard decision decoding of product codes.Abstract:
We show that the recently proposed Fast Fourier Aliasing-based Sparse Transform (FFAST) algorithm for computing the Discrete Fourier Transform (DFT) [1] of signals with a sparse DFT is equivalent to iterative hard decision decoding of product codes. This connection is used to derive the thresholds for sparse recovery based on a recent analysis by Justensen [2] for computing thresholds for product codes. We first extend Justesen's analysis to d-dimensional product codes and compute thresholds for the FFAST algorithm based on this. Additionally, this connection also allows us to analyze the performance of the FFAST algorithm under a burst sparsity model in addition to the uniformly random sparsity model which was assumed in prior work [1].read more
Citations
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Proceedings ArticleDOI
Sketching sparse low-rank matrices with near-optimal sample- and time-complexity
TL;DR: Li et al. as discussed by the authors proposed a sketching scheme and an algorithm that can recover the singular vectors with high probability, with a sample complexity and running time that both depend only on k and not on the ambient dimension n.
Proceedings ArticleDOI
Sketching sparse low-rank matrices with near-optimal sample- and time-complexity
Xiaoqi Liu,Ramji Venkataramanan +1 more
TL;DR: This work proposes a sketching scheme and an algorithm that can recover the singular vectors with high probability, with a sample complexity and running time that both depend only on k and not on the ambient dimension n.
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Sparse Fourier Transform by traversing Cooley-Tukey FFT computation graphs
TL;DR: In this article, a high-dimensional Sparse Fast Fourier Transform (Sparse FFT) toolkit is introduced, which includes a new strategy for exploring a pruned FFT computation tree that reduces the cost of filtering, new structural properties of adaptive aliasing filters, and a novel lazy estimation argument, suited to reducing the time of estimation in FFT tree-traversal approaches.
Proceedings ArticleDOI
FastShare: Scalable Secret Sharing by Leveraging Locality
TL;DR: FastShare as discussed by the authors constructs a signal using the secret and random masks by inserting zeros at judiciously chosen locations, and takes its finite field fast Fourier transform (FFT) to generate the shares.
References
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Nearly Optimal Sparse Fourier Transform
TL;DR: In this paper, the problem of computing the k-sparse approximation to the discrete Fourier transform of an n-dimensional signal was considered, and an O(k log n log(n/k))-time randomized algorithm for general input signals was proposed.
Journal ArticleDOI
Recent Developments in the Sparse Fourier Transform: A compressed Fourier transform for big data
TL;DR: The sparse Fourier transform (SFT) addresses the big data setting by computing a compressed Fouriertransform using only a subset of the input data, in time smaller than the data set size.
Recent Developments in the Sparse Fourier Transform: A compressed Fourier transform for big data
TL;DR: The sparse Fourier transform (SFT) as discussed by the authors addresses the big data setting by computing a compressed Fourier Transform using only a subset of the input data, in time smaller than the data set size.
Journal ArticleDOI
Cyclic product codes
H. Burton,E. Weldon +1 more
TL;DR: A new class of cyclic codes, cyclic product codes, is characterized and is shown to be capable of unambiguous correction of both bursts and random errors and to be a compromise between random and burst-error-correcting codes.
Journal ArticleDOI
Performance of Product Codes and Related Structures with Iterated Decoding
TL;DR: In this paper, the performance of product codes for optical networks has been analyzed and it has been shown that the performance exhibits a threshold that can be estimated from a result about random graphs.