On the Sum Capacity of the Y-Channel

Abstract

A network where three users communicate with each other via a relay is considered. Users do not receive other users' signals via a direct link, and thus the relay is essential for their communication. Each user is assumed to have an individual message to be delivered to each other user. Thus, each user wants to send two messages and to decode two messages. In general, the transmit signals of different nodes can be dependent since they can depend on previously received symbols. We call this case the general case. The sum-capacity is studied, and upper bounds and lower bounds are given. If all nodes have the same power, the sum-capacity is characterized to within a gap of 5/2 bits or a factor of 3 for all values of channel coefficients. This gap is also shown to approach 3/2 bits as the transmit power increases. Moreover, for the symmetric case with equal channel coefficients, the gap is shown to be less than 1 bit. The restricted case is also considered where the transmit signal does not depend on previously received symbols. In this case, the sum-capacity is characterized to within a gap of 2 bits or a factor of 3 for all values of channel coefficients, and approaches 1 bit as the transmit power increases.

arXiv comment12 pages, 8 figures, submitted to ISIT 2011

References in corpus (3)

• Joint Physical Layer Coding and Network Coding for Bi-Directional Relaying
• Divide-and-conquer: Approaching the capacity of the two-pair bidirectional Gaussian relay network
• Capacity Theorems for the AWGN Multi-Way Relay Channel

Cited by in corpus (6)

• Approximate Sum-Capacity of the Y-channel
• Multi-Way Information Exchange Over Completely-Connected Interference Networks with a Multi-Antenna Relay
• The Capacity Region of the Linear Shift Deterministic Y-Channel
• Signal Space Alignment for the Gaussian Y-Channel
• The Degrees of Freedom of the MIMO Y-channel
• The Approximate Capacity Region of the Gaussian Y-Channel