On Channel Inseparability and the DoF Region of MIMO Multi-way Relay Channels

Full-duplex multi-way relaying is a potential solution for supporting high data rates in future Internet-of-Things (IoT) and 5G networks. Thus, in this paper the full-duplex MIMO multi-way channel consisting of 3 users (Y-channel) with $M$ antennas each and a common relay node with $N$ antennas is studied. Each user wants to exchange messages with all the other users via the relay. A transmission strategy is proposed based on channel diagonalization that decomposes the channel into parallel sub-channels, and physical-layer network coding over these sub-channels. It is shown that the proposed strategy achieves the optimal DoF region of the channel if $N\leq M$. Furthermore, the proposed strategy that requires joint encoding over multiple sub-channels is compared to another strategy that encodes over each sub-channel separately. It turns out that coding jointly over sub-channels is necessary for an optimal transmission strategy. This shows that the MIMO Y-channel is inseparable.

[1]  Eduard A. Jorswieck,et al.  Spectral and energy efficiency in 3-way relay channels with circular message exchanges , 2014, 2014 11th International Symposium on Wireless Communications Systems (ISWCS).

[2]  Mohammed Nafie,et al.  Achievable degrees of freedom region of MIMO relay networks using Detour Schemes , 2014, 2014 IEEE International Conference on Communications (ICC).

[3]  Syed Ali Jafar,et al.  Parallel Gaussian Interference Channels Are Not Always Separable , 2009, IEEE Transactions on Information Theory.

[4]  Dave Evans,et al.  How the Next Evolution of the Internet Is Changing Everything , 2011 .

[5]  F. Al-Qahtani,et al.  Optimal relay selection for decode-and-forward opportunistic relaying , 2013, 2013 1st International Conference on Communications, Signal Processing, and their Applications (ICCSPA).

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

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

[8]  Abbas El Gamal,et al.  Capacity theorems for the relay channel , 1979, IEEE Trans. Inf. Theory.

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

[10]  Aydin Sezgin,et al.  Simultaneous Diagonalization: On the DoF Region of the K-user MIMO Multi-way Relay Channel , 2014, ArXiv.

[11]  Syed Ali Jafar,et al.  Interference Alignment and Spatial Degrees of Freedom for the K User Interference Channel , 2007, 2008 IEEE International Conference on Communications.

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

[13]  Michael Gastpar,et al.  Compute-and-Forward: Harnessing Interference Through Structured Codes , 2009, IEEE Transactions on Information Theory.

[14]  Sae-Young Chung,et al.  Capacity Bounds for Two-Way Relay Channels , 2008, 2008 IEEE International Zurich Seminar on Communications.

[15]  Aydin Sezgin,et al.  The degrees of freedom of the MIMO Y-channel , 2013, 2013 IEEE International Symposium on Information Theory.

[16]  Aydin Sezgin,et al.  Approximate Sum-Capacity of the Y-Channel , 2013, IEEE Transactions on Information Theory.

[17]  Mohamed-Slim Alouini,et al.  Joint opportunistic scheduling and network coding for bidirectional relay channel , 2013, 2013 IEEE International Symposium on Information Theory.

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

[19]  Andrea J. Goldsmith,et al.  The Multiway Relay Channel , 2013, IEEE Transactions on Information Theory.

[20]  Mohammed Nafie,et al.  On the deterministic multicast capacity of bidirectional relay networks , 2010, 2010 IEEE Information Theory Workshop.

[21]  Mohamed-Slim Alouini,et al.  On the achievable degrees of freedom of alternate MIMO relaying with multiple AF relays , 2012, Third International Conference on Communications and Networking.

[22]  Aydin Sezgin,et al.  Signal space alignment for the Gaussian Y-channel , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[23]  Aydin Sezgin,et al.  Capacity region of the deterministic multi-pair bi-directional relay network , 2009, 2009 IEEE Information Theory Workshop on Networking and Information Theory.

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

[25]  Lawrence Ong,et al.  On the Equal-Rate Capacity of the AWGN Multiway Relay Channel , 2012, IEEE Transactions on Information Theory.