Achievable Degrees of Freedom on K-user Y Channels
Kwang‐Won Lee, Namyoon Lee, Inkyu Lee · IEEE Transactions on Wireless Communications · 2012
In this paper, we consider K-user Y channels where K users simultaneously exchange messages with each other via an intermediate relay. Degrees of freedom (DOF) of Y channels with multiple antennas is not known in general. Investigation of the feasibility conditions of signal space alignment for network coding is an initial step for addressing this open problem. We verify that when user i with M-i antennas sends K-1 independent messages to the other users through a relay with N antennas and each message achieves the DOF of d, the total DOF of dK(K-1) is attained if M-i >= d(K - 1), N >= dK(K-1)/2 and N infinity. Also for Y channels where all nodes have a single antenna, we show that the DOF of 2 is achieved regardless of the number of users by using the rational dimension framework.