The degrees of freedom of the MIMO Y-channel

The degrees of freedom (DoF) of the MIMO Y-channel, a multi-way communication network consisting of 3 users and a relay, are characterized for arbitrary number of antennas. The converse is provided by cut-set bounds and novel genie-aided bounds. The achievability is shown by a scheme that uses beamforming to establish network coding on-the-fly at the relay in the uplink, and zero-forcing pre-coding in the downlink. It is shown that the network has min{2M2+2M3, M1+ M2 + M3,2N} DoF, where Mj and N represent the number of antennas at user j and the relay, respectively. Thus, in the extreme case where M1+M2+M3 dominates the DoF expression and is smaller than N, the network has the same DoF as the MAC between the 3 users and the relay. In this case, a decode and forward strategy is optimal. In the other extreme where 2N dominates, the DoF of the network is twice that of the aforementioned MAC, and hence network coding is necessary. As a byproduct of this work, it is shown that channel output feedback from the relay to the users has no impact on the DoF of this channel.

[1]  Syed A. Jafar,et al.  Interference Alignment: A New Look at Signal Dimensions in a Communication Network , 2011, Found. Trends Commun. Inf. Theory.

[2]  A. Wittneben,et al.  Spectral Efficient Signaling for Half-duplex Relay Channels , 2005, Conference Record of the Thirty-Ninth Asilomar Conference onSignals, Systems and Computers, 2005..

[3]  Sae-Young Chung,et al.  Capacity of the Gaussian Two-way Relay Channel to within 1/2 Bit , 2009, ArXiv.

[4]  Joohwan Chun,et al.  Degrees of Freedom of the MIMO Y Channel: Signal Space Alignment for Network Coding , 2010, IEEE Transactions on Information Theory.

[5]  Thomas M. Cover,et al.  Elements of Information Theory: Cover/Elements of Information Theory, Second Edition , 2005 .

[6]  Natasha Devroye,et al.  Lattice coding for the Two-way Two-relay channel , 2013, 2013 IEEE International Symposium on Information Theory.

[7]  Sang Joon Kim,et al.  Comparison of bi-directional relaying protocols , 2008, 2008 IEEE Sarnoff Symposium.

[8]  Aydin Sezgin,et al.  On the sum capacity of the Y-channel , 2011, 2011 Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR).

[9]  J. Nayak,et al.  Rate regions for the separated two-way relay channel , 2008, 2008 46th Annual Allerton Conference on Communication, Control, and Computing.

[10]  Andrea J. Goldsmith,et al.  The multi-way relay channel , 2009, 2009 IEEE International Symposium on Information Theory.

[11]  Lawrence Ong,et al.  Capacity Theorems for the AWGN multi-way relay channel , 2010, 2010 IEEE International Symposium on Information Theory.

[12]  Tobias J. Oechtering,et al.  Broadcast Capacity Region of Two-Phase Bidirectional Relaying , 2007, IEEE Transactions on Information Theory.

[13]  Aydin Sezgin,et al.  Divide-and-Conquer: Approaching the Capacity of the Two-Pair Bidirectional Gaussian Relay Network , 2012, IEEE Transactions on Information Theory.

[14]  Aydin Sezgin,et al.  Information Theory Capacity of the two-way relay channel within a constant gap , 2010, Eur. Trans. Telecommun..

[15]  Aydin Sezgin,et al.  Bidirectional multi-pair network with a MIMO relay: Beamforming strategies and lack of duality , 2010, 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[16]  Tetsunao Matsuta,et al.  国際会議開催報告:2013 IEEE International Symposium on Information Theory , 2013 .

[17]  Sae-Young Chung,et al.  Capacity of the Gaussian Two-Way Relay Channel to Within ${1\over 2}$ Bit , 2009, IEEE Transactions on Information Theory.