Patent ID: 8413019

Claim:
A system comprising: a first computer configured as an encoding device for transmitting data via a transmission medium, the transmitting comprising: encoding the data using a linear code, the encoded data represented by an original vector y; and providing the original vector y to the transmission medium; and a second computer configured as a decoding device for receiving and recovering the original vector y from data received via the transmission medium, the received data comprising a corrupted vector y′ corrupted by one or more errors introduced in the transmission medium, the recovering comprising: correcting the corrupted vector y′ by solving the convex optimization problem min x ∈ R n ⁢  y - Ax  l 1 using a linear program wherein A is a coding matrix expressing the linear code, and l 1 represents a norm such that  x  l 1 := ∑ i ⁢  x i  .