TY - JOUR
AU - Roberto Nóbrega
AU - Chen Feng
AU - Danilo Silva
AU - Bartolomeu Uchôa-Filho
PY - 2017/09/17
Y2 - 2020/09/25
TI - On Multiplicative Matrix Channels over Finite Chain Rings
JF - Journal of Communication and Information Systems
JA - JCIS
VL - 32
IS - 1
SE - Regular Papers
DO - 10.14209/jcis.2017.10
UR - https://jcis.sbrt.org.br/jcis/article/view/471
AB - 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 Y = AX, where X and Y are the input and output matrices, respectively, and A 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 A and X are independent. Besides that, no restrictions on the statistics of A 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.
ER -