Network vs Wireless Channel-I Min-cut =1 x R Rx y2 R Network with multiple unicasts 21=m1(x)X1+m2(x)X2+m3(x)X3 yi= h1i 1+h2i C2+h3i3+n Transfer function introduced by network Channel gain: introduced by nature 6
6 Network vs. Wireless Channel - I Network with multiple unicasts SISO Channel gain: introduced by nature 𝑋1 𝑋2 𝑋3 𝑍2 𝑍1 𝑍3 𝑥1 𝑥2 𝑥3 𝑦1 𝑦2 𝑦3 Transfer function: introduced by network Min-cut = 1
Networks vs, ireless Channel-II Min -cut>1 Z 3 Network with multiple unicasts MIMO Z1=M1X1+M2X2+M32X3 yi=LixI +H2i X2+H3ix3+n Transfer matrⅸx Channel matrix
7 Networks vs. Wireless Channel - II Network with multiple unicasts MIMO 𝐗1 𝐗2 𝐗3 𝐙2 𝐙1 𝐙3 𝐱1 𝐱2 𝐱3 𝐲1 𝐲2 𝐲3 Min-cut > 1 Transfer matrix Channel matrix
Interference ali ignment Common problem Too MANy unknowns Solution: Align interferences to reduce the number of unknowns Benef计: Everyone gets one half of the cake V. Cadambe and S Jafar, " Interference Alignment and Degrees of Freedom of the K-User Interference Channel
8 Interference Alignment Common problem: Too MANY unknowns! Solution: Align interferences to reduce the number of unknowns V. Cadambe and S. Jafar, “Interference Alignment and Degrees of Freedom of the K-User Interference Channel” Benefit: Everyone gets one half of the cake
Brief Intro of ia o Originally introduced by cadambe& jafar pproaches Asymptotic alignment, Ergodic alignment Lattice alignment Blind alignment pplIcaTions K-user wireless interference channel K-user Mimo interference channe Cellular networks Multi-hop interference networks Exact repair in distributed storage Syed A Jafar, " Interference Alignment -A New Look at Signal Dimensions in a Communication Network
9 Brief Intro of IA o Originally introduced by Cadambe & Jafar o Approaches: • Asymptotic alignment, • Ergodic alignment, • Lattice alignment, • Blind alignment o Applications • K-user wireless interference channel, • K-user MIMO interference channel, • Cellular networks, • Multi-hop interference networks, • Exact repair in distributed storage Syed A. Jafar, “Interference Alignment — A New Look at Signal Dimensions in a Communication Network
Network Is Not wireless channel Zi=mi(x)X1+mi2(x)X2+mi3(x)X3 yi=h1:1+h2:2+h3i3+n o Xi, Zi symbols from finite field I o yi, xi: real complex numbers o mii(x): polynomial of coding variables I o hij; structureless 10
10 Network Is NOT Wireless Channel o 𝑋𝑖 , 𝑍𝑖 : symbols from finite field o 𝑚𝑖𝑗(𝐱): polynomial of coding variables o 𝑦𝑖 , 𝑥𝑖 : real & complex numbers o ℎ𝑖𝑗: structureless