Random channel coding and blind deconvolution
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
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EURASIP Journal on Advances in Signal Processing - Special issue on robust processing of nonstationary signals
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Automatica (Journal of IFAC)
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Robust Estimation for an Inverse Problem Arising in Multiview Geometry
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This paper discusses a stylized communications problem where one wishes to transmit a real-valued signal (a block of pieces of information) to a remote receiver. We ask whether it is possible to transmit this information reliably when a fraction of the transmitted codeword is corrupted by arbitrary gross errors, and when in addition, all the entries of the codeword are contaminated by smaller errors (e.g., quantization errors). We show that if one encodes the information as where is a suitable coding matrix, there are two decoding schemes that allow the recovery of the block of pieces of information with nearly the same accuracy as if no gross errors occurred upon transmission (or equivalently as if one had an oracle supplying perfect information about the sites and amplitudes of the gross errors). Moreover, both decoding strategies are very concrete and only involve solving simple convex optimization programs, either a linear program or a second-order cone program. We complement our study with numerical simulations showing that the encoder/decoder pair performs remarkably well.