Allerton 2015 Paper Abstract

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Paper ThD4.3

Thenkarai Janakiraman, Nagaraj (Texas A & M university, College Station), Emmadi, Santosh (Texas A&M University, College Station), Narayanan, Krishna (Texas A&M University), Ramchandran, Kannan (UC Berkeley)

Exploring Connections between Sparse Fourier Transform Computation and Decoding of Product Codes

Scheduled for presentation during the Regular Session "Coding Techniques and Applications II" (ThD4), Thursday, October 1, 2015, 16:10−16:30, Pine

53rd Annual Allerton Conference on Communication, Control, and Computing, Sept 29-Oct 2, 2015, Allerton Park and Retreat Center, Monticello, IL, USA

This information is tentative and subject to change. Compiled on November 19, 2019

Keywords Sparse Data Analysis, Coding Techniques and Applications, Coding Theory

Abstract

We show 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. This connection is used to derive the thresholds for sparse recovery based on a recent analysis by Justensen for computing thresholds for product codes. We first extend Justesenís 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

 

 

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