On multiplicative matrix channels over finite chain rings

Motivated by nested-lattice-based physical-layer network coding, this paper considers communication in multiplicative matrix channels over finite chain rings. Such channels are defined by the law Y = AX, where X and Y are the input and output matrices, respectively, and A is called the transfer matrix. We assume that the instances of the transfer matrix are unknown to the transmitter, but available at the receiver. As contributions, we obtain a closed-form expression for the channel capacity, and we propose a coding scheme that can achieve this capacity with polynomial time complexity. Our results extend the corresponding ones for finite fields.