Error correction and convex programming

This article discusses a recently proposed error correction method involving convex optimization [1]. From an encoded and corrupted real‐valued message, a receiver would like to determine the original message. A few entries of the encoded message are corrupted arbitrarily (which we call gross errors) and all the entries of the encoded message are corrupted slightly. We show that it is possible to recover the message with nearly the same accuracy as in the setting where no gross errors occur.