Error correction via linear programming

Suppose we wish to transmit a vector f 2 Rn reliably. A frequently discussed approach consists in encoding f with an m by n coding matrix A. Assume now that a fraction of the entries of Af are corrupted in a completely arbitrary fashion. We do not know which entries are aected nor do we know how they are aected. Is it possible to recover f exactly from the corrupted m-dimensional vector y? This paper proves that under suitable conditions on the coding matrix A, the input f is the unique solution to the '1-minimization problem (kxk'1 := P i |xi|)