Compressed network coding: Overcome all-or-nothing problem in finite fields

In this paper, we consider a delay-sensitive data transmission strategy based on network coding technique in finite fields over error-prone networks. In order to solve all-or-nothing problem inherited from network coding, compressed network coding is proposed by jointly considering network coding techniques and compressed sensing technique. While network coding techniques have been jointly used with the compressed sensing techniques, network coding operations are performed in the field of real numbers, and thus, the payload of transmitted data can be enlarged as the data traverse more hops in networks. In this paper, however, we propose to use network coding techniques in finite fields, such that the size of payload does not increase as more hops are traversed. With the help of compressed sensing technique, a destination node is able to approximately recover the source data based on l₁-norm minimization approach, in case of innovative packet loss. It is analytically shown that the payload size of the proposed approach is always smaller than that of the conventional approach, while the proposed approach can achieve comparable decoding performances. We evaluate the effectiveness of the proposed approach based on an illustrative application of image delivery system.