Communication over Finite-Chain-Ring Matrix Channels

Date Added: Apr 2013
Format: PDF

Though network coding is traditionally performed over finite fields, recent work on nested-lattice-based network coding suggests that, by allowing network coding over finite chain rings, more efficient physical-layer network coding schemes can be constructed. This paper considers the problem of communication over the finite-chain-ring matrix channel Y = AX + BZ, where X is the channel input, Y is the channel output, Z is random noise, and A and B are random transfer matrices. Tight capacity results are obtained and simple polynomial-complexity capacity-achieving coding schemes are provided under certain distributions of A, B, and Z, extending the work of Silva, Kschischang and Kotter (2010), who handled the case of finite fields.