On network error correction under a secret key model

This work presents an error control scheme for noncoherent linear network coding under an adversarial error model. The scheme relies on the assumption that the transmitter and the receiver share a random key that is secret from the adversary. The scheme is shown to achieve, asymptotically in the packet length, the highest possible rate under this model-which is significantly higher than what can be achieved without a shared key. Previous approaches to key-based error control required either an asymptotically large field or an impractically long key. The proposed scheme removes both restrictions, and is therefore suitable for practical applications of network coding. The scheme is based on MRD codes and makes crucial use of extension field ideas.