Error correction via smoothed L0-norm recovery

Channel coding has been considered as a classical approach to overcome corruptions occurring in some elements of input signal which may lead to loss of some information. Proper redundancies are added to the input signal to improve the capability of detecting or even correcting the corrupted signal. A similar scenario may happen dealing with real-field numbers rather than finite-fields. This paper considers a way to reconstruct an exact version of a corrupted signal by using an encoded signal with proper number of redundancies. The proposed algorithm uses Graduated Non-Convexity method beside using a smoothed function instead of ℓ⁰-norm to correct all the corrupted elements. Simulations show that our proposed algorithm substantially improves the probability of exact recovery in comparison to previous algorithms.