On the Capacity of Multiplicative Finite-Field Matrix Channels
This paper deals with the multiplicative finite-field matrix channel, a discrete memory-less channel whose input and output are matrices (over a finite field) related by a multiplicative transfer matrix. The authors' model allows this transfer matrix to have any rank, while assuming that all transfer matrices with the same rank are equi-probable. A tight upper bound on the capacity is also derived, and for the special case of constant-rank input, they obtain an exact formula. Several existing results can be obtained as special cases of their approach. In addition, they prove that the well-known approach of treating inputs and outputs as subspaces is information-lossless even in this more general case.