TY - JOUR
T1 - Achievable degrees of freedom on K-user y channels
AU - Lee, Kwangwon
AU - Lee, Namyoon
AU - Lee, Inkyu
N1 - Funding Information:
Manuscript received June 24, 2011; revised November 2, 2011; accepted December 19, 2011. The associate editor coordinating the review of this paper and approving it for publication was X. Xiang-Gen. K. Lee and I. Lee are with the School of Electrical Engineering, Korea University, Seoul, Korea (e-mail: {kwangwonlee, inkyu}@korea.ac.kr). N. Lee is with the University of Texas, Austin, USA (e-mail: namy-oon.lee@gmail.com). The material in this paper was presented in part at the IEEE ICC, Kyoto, Japan, June 2011. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2010-0017909). Digital Object Identifier 10.1109/TWC.2012.012712.111194
PY - 2012/3
Y1 - 2012/3
N2 - 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 < min{ i+M j-d | forall i ≠j}. It is accomplished by adopting the signal space alignment for the network coding during both the multiple access phase and the broadcast phase. It is shown that the proposed scheme obtains not only a network coding gain but also an alignment gain in terms of the normalized DOF, as K → ∞. 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.
AB - 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 < min{ i+M j-d | forall i ≠j}. It is accomplished by adopting the signal space alignment for the network coding during both the multiple access phase and the broadcast phase. It is shown that the proposed scheme obtains not only a network coding gain but also an alignment gain in terms of the normalized DOF, as K → ∞. 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.
KW - Degrees of freedom
KW - Y channels
KW - interference alignment
KW - network coding
UR - http://www.scopus.com/inward/record.url?scp=84863373526&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84863373526&partnerID=8YFLogxK
U2 - 10.1109/TWC.2012.012712.111194
DO - 10.1109/TWC.2012.012712.111194
M3 - Article
AN - SCOPUS:84863373526
VL - 11
SP - 1210
EP - 1219
JO - IEEE Transactions on Wireless Communications
JF - IEEE Transactions on Wireless Communications
SN - 1536-1276
IS - 3
M1 - 6144762
ER -