Rank deficient decoding for arithmetic subspace network coding

Abstract

In arithmetic network coding (ANC), finite field operations are replaced by real or complex arithmetic operations. This has applications in physical layer network coding or in multi-resolution multicast, where users with a higher download capacity experience a better quality of service. A major problem in random ANC is that the condition number of the network grows quickly with the network size, hence, noise can cause many errors in larger networks. An efficient solution for error correction in network coding is subspace coding. However, existing subspace coding solutions are based on finite field operations and cannot be used with ANC. Some of the difficulties of applying subspace coding to ANC are: (i) there are infinite subspaces to choose from; (ii) the effect of noise is on all links, where the noise strength increases hop by hop; and (iii) the decoding algorithms of ANC and subspace decoding are very different. In this work, we develop a subspace arithmetic network coding framework. We first model the network noise from which we then develop a decoding algorithm. Our simulation results show the success of our proposed method over conventional ANC.