Rank-matching for multihop multiflow

© 2014 IEEE. Seeking fundamental insights into multi-hop multi-flow networks we study the simplest non-trivial setting, a 2 × 2 × 2 MIMO interference network comprised of two sources, two relays and two destinations, wherein all nodes have M antennas, all first-hop channels are of rank D1, and all second hop channels are of rank D2. For this setting, we show that the optimal sum DoF is min(4D1, 4D2, 2M - |D1 - D2|). While 4D1, 4D2 are the obvious min-cut bottlenecks that are active when either hop is severely rank-deficient, what is remarkable is that under moderate rank-deficiencies the DoF are limited not by the higher or the lower of the two ranks D1, D2, but only by the difference of the two ranks |D1 - D2|. This suggests an interesting 'rank-matching' design principle for multi-hop networks, reminiscent of 'impedance matching', wherein the goal is not necessarily to increase or decrease the rank of each hop, but rather to use linear processing at intermediate hops to create effectively a two-hop setting with matching ranks

Rank-matching for multihop multiflow

Abstract—Seeking fundamental insights into multi-hop multi-flow networks we study the simplest non-trivial setting, a 2⇥2⇥2 MIMO interference network comprised of two sources, two relays and two destinations, wherein all nodes have M antennas, all first-hop channels are of rank D1, and all second hop channels are of rank D2. For this setting, we show that the optimal sum DoF is min(4D1, 4D2, 2M |D1 D2|). While 4D1, 4D2 are the obvious min-cut bottlenecks that are active when either hop is severely rank-deficient, what is remarkable is that under moderate rank-deficiencies the DoF are limited not by the higher or the lower of the two ranks D1, D2, but only by the difference of the two ranks |D1 D2|. This suggests an interesting “rank-matching ” design principle for multi-hop networks, reminiscent of “impedance matching”, wherein the goal is not necessarily to increase or decrease the rank of each hop, but rather to use linear processing at intermediate hops to create effectively a two-hop setting with matching ranks. I

Rank-matching for multihop multiflow

© 2014 IEEE. Seeking fundamental insights into multi-hop multi-flow networks we study the simplest non-trivial setting, a 2 × 2 × 2 MIMO interference network comprised of two sources, two relays and two destinations, wherein all nodes have M antennas, all first-hop channels are of rank D1, and all second hop channels are of rank D2. For this setting, we show that the optimal sum DoF is min(4D1, 4D2, 2M - |D1 - D2|). While 4D1, 4D2 are the obvious min-cut bottlenecks that are active when either hop is severely rank-deficient, what is remarkable is that under moderate rank-deficiencies the DoF are limited not by the higher or the lower of the two ranks D1, D2, but only by the difference of the two ranks |D1 - D2|. This suggests an interesting 'rank-matching' design principle for multi-hop networks, reminiscent of 'impedance matching', wherein the goal is not necessarily to increase or decrease the rank of each hop, but rather to use linear processing at intermediate hops to create effectively a two-hop setting with matching ranks

IEEE Transactions On Information Theory: Vol. 61, No.9, September 2015

1. Covering point pattern / A. Lapidoth, A. Malar, L. Wang 2. New nonasymptotic channel coding theorems for structured codes / E. -H. Yang, J. Meng 3. A General formula for the mismatch capacity / A. Somekh-Baruch 4. On the dispersions of the Gel\u27fand-pinsker channel and dirty paper coding / J. Scarlett 5. Gaussian state amplification with noisy observations / C. Tian, B. Bandemer, S. Shamai 6. Optimum power control at finite blocklength / W. Yang, G. Craire, G. Durisi, Y. Polyanskiy 7. Outer bounds on the admissible source region for broadcast channels with correlated sources / K. Khezeli, J. Chen 8. On the diversity-multiplexing tradeoff of unconstrained multiple-access channels / Y. Yona, M. Feder 9. Gaussian interface channel with intermmittent feedback / C. Karakus, I. -H. Wang, S. Diggavi 10. Virtual full-duplex relaying with half-duplex relays / S. -N. Hong, G. Caire 11. Capacity approximations for gaussian relay networks / R. Kolte, A. Ozgur, A. El Gamal 12. Beyond scaling laws: on the rate performance of dense device-to-device wirelees networks / S. -N. Hong, G. Caire 13. Rank matching for multihop multiflow / S. Sun, S. R. Krishnamurthy, S. A. Jafar 14. Interactive computation of type-threshold functions in collocated gaussian networks / C. -Y. Wang, S. -W. Jeon, M. Gastpar 15. CSMA using the bethe approximation: Scheduling and ulility maximization / S. - Y. Yun, J. Shin, Y. Jitu H Et