@article{Nóbrega_Feng_Silva_Uchôa-Filho_2017, title={On Multiplicative Matrix Channels over Finite Chain Rings}, volume={32}, url={https://jcis.sbrt.org.br/jcis/article/view/471}, DOI={10.14209/jcis.2017.10}, abstractNote={Motivated by physical-layer network coding, this paper considers communication in multiplicative matrix channels over finite chain rings. Such channels are defined by the law <em>Y = AX</em>, where <em>X</em> and <em>Y</em> are the input and output matrices, respectively, and <em>A</em> is called the transfer matrix. It is assumed a coherent scenario in which the instances of the transfer matrix are unknown to the transmitter, but available to the receiver. It is also assumed a memoryless channel, and that <em>A</em> and <em>X</em> are independent. Besides that, no restrictions on the statistics of <em>A</em> are imposed. As contributions, a closed-form expression for the channel capacity is obtained, and a coding scheme for the channel is proposed. It is then shown that the scheme can achieve the capacity with polynomial time complexity and can provide correcting guarantees under a worst-case channel model. The results in the paper extend the corresponding ones for finite fields.}, number={1}, journal={Journal of Communication and Information Systems}, author={Nóbrega, Roberto W. and Feng, Chen and Silva, Danilo and Uchôa-Filho, Bartolomeu F.}, year={2017}, month={Sep.} }