De nition of feasible rate vectors in .NET Print Denso QR Bar Code in .NET De nition of feasible rate vectors 19.3.2 De nition of feasible rate vectorsQr Bidimensional Barcode barcode library with .netuse visual studio .net qr-code development toencode qr barcode for .netDe nition 1 Consider a wireless network with multiple source destination pairs (s , d ), = 1, . . . , m, with s = d , and (s , d ) = (s j , d j ) for = j. Let S := {s , = 1, . . . , m} denote the set of source nodes. The number of nodes in S may be less than m, since we allow a noderead qr-codes for .netUsing Barcode scanner for .net framework Control to read, scan read, scan image in .net framework applications.NETWORK INFORMATION THEORY Barcode barcode library for .netusing .net framework toincoporate barcode with asp.net web,windows applicationto have originating traf c for several destinations. Then a [(2TR1 , . . . , 2TRm ), T, Pe(T ) ] code with total power constraint Ptotal consists of the following: (1) m independent random variables W (transmitted words TRl bits long) with P(Wl = kl ) = 1/2T Rl , for any k {1, 2, . . . , 2TR }, = 1, . . . , m. For any i S, let Wi := R {W : s = i} and Ri :=Bar Code barcode library for .netusing visual .net crystal toincoporate barcode in asp.net web,windows application{ :s =i}Control qr code size with c#to draw qr code and qr code jis x 0510 data, size, image with c# barcode sdk(2) Functions f i,t : R {1, 2, . . . , 2T Ri } R, t = 1, 2, . . . , T, for the source nodes i S and f j,t : Rt 1 R, t = 2, . . . , T , for all the other nodes j S, such / thatControl denso qr bar code size in .net qr barcode size in .net X i (t) = f i,t (Yi (1), . . . , Yi (t 1), Wi ), t = 1, 2, . . . , T X j (1) = 0, X j (t) = f j,t (Y j (1), . . . , Y j (t 1)), t = 2, 3, . . . , T such that the following total power constraint holds: 1 T (3) m decoding functions g : RT {1, 2, . . . , |W d |} {1, 2, . . . , 2TR } for the destination nodes of the m source-destination pairs {(s , d ), = 1, . . . , m}, where |W d | is the number of different values W d can take. Note that Wd may be empty. (4) The average probability of error: Pe(T ) := Prob (W1 , W2 , . . . , Wm ) = (W1 , W2 , . . . , Wm ) where W := g (YdT , Wd ), with YdT := Yd (1), Yd (2), . . . , Yd (T ) . (19.48)Qr Codes barcode library for visual basic.netgenerate, create quick response code none on vb projectsX i2 (t) Ptotal Pdf417 2d Barcode maker for .netusing vs .net crystal toprint pdf-417 2d barcode for asp.net web,windows applicationt=1 i N .net Framework Crystal 2d matrix barcode printing with .netuse .net vs 2010 crystal 2d barcode drawer toinsert 2d matrix barcode on .net(19.47)Data Matrix ECC200 encoding in .netuse .net framework crystal datamatrix 2d barcode encoding toincoporate ecc200 in .netDe nition 2 A rate vector (R1 , . . . , Rm ) is said to be feasible for the m source-destination pairs (s , d ), = 1, . . . , m, with total power constraint Ptotal , if there exists a sequence of [(2TR1 , . . . , 2TRm ), T, Pe(T ) ] codes satisfying the total power constraint Ptotal , such that Pe(T ) 0 as T . The preceding de nitions are presented with total power constraint Ptotal . If an individual power constraint Pind is placed on each node, then Equation (19.47) should be modi ed: 1 TAccess quick response code with .netusing barcode integrating for visual studio .net crystal control to generate, create qr code jis x 0510 image in visual studio .net crystal applications.X i2 (t) Pind ,Visual .net Crystal isbn integrating with .netgenerate, create isbn - 13 none for .net projectsfor i N Control code 3 of 9 data in c# code 3/9 data on visual c#(19.49)Control ucc - 12 size with office word gs1128 size for wordand correspondingly modify the rest of the de nitions to de ne the set of feasible rate vectors under an individual power constraint.Display data matrix ecc200 with visual basic.netuse visual studio .net barcode data matrix encoding togenerate datamatrix 2d barcode with vb.netINFORMATION THEORY AND NETWORK ARCHITECTURES Control ean-13 size in microsoft excelto generate ean-13 supplement 2 and ean13 data, size, image with office excel barcode sdk19.3.3 The transport capacity The capacity region, is the closure of the set of all such feasible vector rates. As in Section 19.2 we will, focus mainly on the distance-weighted sum of rates. De nition 3 As in Section 19.2, the network s transport capacity CT isExcel Spreadsheets pdf417 generation for excel spreadsheetsusing excel todraw pdf 417 in asp.net web,windows applicationCT :=Control code-128c data in java code 128 code set b data with java(R1 ,...,Rm ) feasible Control qr codes image on .netuse asp.net website qr-code implement todraw denso qr bar code on .netR EAN 13 barcode library on .netgenerate, create european article number 13 none in .net projectswhere := s d is the distance between s and d , and R := Rs d . In the following, due to limited space, a number of results from information theory will be presented without the formal proof. For more details the reader is referred to Xie and Kumar . 19.3.4 Upper bounds under high attenuation (r1) The transport capacity is bounded by the network s total transmission power in media with > 0 or > 3. For a single link (s, d), the rate R is bounded by the received power at d. In wireless networks, owing to mutual interference, the transport capacity is upper-bounded by the total transmitted power Ptotal used by the entire network. In any planar network, with either positive absorption, i.e. > 0, or with path loss exponent > 3 CT where c1 ( , , min ) Ptotal 2 (19.50) 2 +7 log ee min /2 (2 e min /2 ) 2 , if > 0 2 min 2 +1 (1 e min /2 ) c1 ( , , min ) := (19.51) 22 +5 (3 8) log e , if = 0 and > 3 ( 2)2 ( 3) min 2 1(r2) The transport capacity follows an O(n) scaling law under the individual power constraint, in media with > 0 or > 3. Consider any planar network under the individual power constraint Pind . Suppose that either there is some absorption in the medium, i.e. > 0, or there is no absorption at all but the path loss exponent > 3. Then its transport capacity is upper-bounded as follows: c1 ( , , min )Pind n 2 where c1 ( , , min ) is given by Equation (19.51). As in the previous section we use notation: CT f = O(g) if lim sup [ f (n)/g(n)] < +