Cognitive Wyner Networks with Clustered Decoding

We study an interference network where equally-numbered transmitters and receivers lie on two parallel lines, each transmitter opposite its intended receiver. We consider two short-range interference models: the "asymmetric network," where the signal sent by each transmitter is interfered only by the signal sent by its left neighbor (if present), and a "symmetric network," where it is interfered by both its left and its right neighbors. Each transmitter is cognizant of its own message, the messages of the $t_\ell$ transmitters to its left, and the messages of the $t_r$ transmitters to its right. Each receiver decodes its message based on the signals received at its own antenna, at the $r_\ell$ receive antennas to its left, and the $r_r$ receive antennas to its right. For such networks we provide upper and lower bounds on the multiplexing gain, i.e., on the high-SNR asymptotic logarithmic growth of the sum-rate capacity. In some cases our bounds meet, e.g., for the asymmetric network. Our results exhibit an equivalence between the transmitter side-information parameters $t_\ell, t_r$ and the receiver side-information parameters $r_\ell, r_r$ in the sense that increasing/decreasing $t_\ell$ or $t_r$ by a positive integer $\delta$ has the same effect on the multiplexing gain as increasing/decreasing $r_\ell$ or $r_r$ by $\delta$. Moreover---even in asymmetric networks---there is an equivalence between the left side-information parameters $t_\ell, r_\ell$ and the right side-information parameters $t_r, r_r$.