Point-to-Point Links. Problem: Consecutive 1s or 0s. Alternative Encodings. Encoding. Signals propagate over a physical medium

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Randolph Williams
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1 Encdng Pn--Pn Lnks Oln Encdng Frang Errr Dcn Sldng Wndw Algrh Sgnals prpaga vr a physcal d dla lcragnc wavs.g., vary vlag Encd bnary daa n sgnals.g., 0 as lw sgnal and 1 as hgh sgnal knwn as Nn-Rrn zr (NRZ) Bs NRZ Sprng 2005 CS Sprng 2005 CS Prbl: Cnscv 1s r 0s Lw sgnal (0) ay b nrprd as n sgnal Hgh sgnal (1) lads basln wandr Unabl rcvr clck Alrnav Encdngs Nn-rrn Zr Invrd (NRZI) ak a ransn fr crrn sgnal ncd a n; say a crrn sgnal ncd a zr slvs h prbl f cnscv ns Manchsr rans XOR f h NRZ ncdd daa and h clck nly 50% ffcn (b ra = 1/2 bad ra) Sprng 2005 CS Sprng 2005 CS 461 4

2 Encdngs (cn) Encdngs (cn) Bs NRZ Clck Manchsr B/5B vry 4 bs f daa ncdd n a 5-b cd 5-b cds slcd hav n r han n ladng 0 and n r han w ralng 0s hs, nvr g r han hr cnscv 0s rslng 5-b cds ar ransd sng NRZI achvs 80% ffcncy NRZI Sprng 2005 CS Sprng 2005 CS Frang Brak sqnc f bs n a fra ypcally plnd by nwrk adapr Snnl-basd Apprachs dlna fra wh spcal parn: g., HDLC, SDLC, PPP Nd A Bs Adapr Adapr Nd B Fras Bgnnng sqnc Hadr Bdy CRC Endng sqnc prbl: spcal parn appars n h paylad sln: b sffng sndr: nsr 0 afr fv cnscv 1s rcvr: dl 0 ha fllws fv cnscv 1s Sprng 2005 CS Sprng 2005 CS 461 8

3 Apprachs (cn) Cnr-basd ncld paylad lngh n hadr.g., DDCMP Apprachs (cn) Clck-basd ach fra s 125s lng.g., SONE: Synchrns Opcal Nwrk SS-n (SS-1 = Mbps) Cn Hadr Bdy CRC Ovrhad Paylad SS -1 SS -1 SS -1 prbl: cn fld crrpd sln: cach whn CRC fals 9 rws Hdr SS -3c 90 clns Sprng 2005 CS Sprng 2005 CS Cyclc Rdndancy Chck Add k bs f rdndan daa an n-b ssag wan k << n.g., k = 32 and n = 12,000 (1500 bys) Rprsn n-b ssag as n-1 dgr plynal.g., MSG= as M(x) = x 7 + x 4 + x 3 + x 1 L k b h dgr f s dvsr plynal.g., C(x) = x 3 + x CRC (cn) rans plynal P(x) ha s vnly dvsbl by C(x) shf lf k bs,.., M(x)x k sbrac randr f M(x)x k / C(x) fr M(x)x k Rcvr plynal P(x) + E(x) E(x) = 0 pls n rrrs Dvd (P(x) + E(x)) by C(x); randr zr f: E(x) was zr (n rrr), r E(x) s xacly dvsbl by C(x) Sprng 2005 CS Sprng 2005 CS

4 Slcng C(x) All sngl-b rrrs, as lng as h x k and x 0 rs hav nn-zr cffcns. All dbl-b rrrs, as lng as C(x) cnans a facr wh a las hr rs Any dd nbr f rrrs, as lng as C(x) cnans h facr (x + 1) Any brs rrr (.., sqnc f cnscv rrr bs) fr whch h lngh f h brs s lss han k bs. Ms brs rrrs f largr han k bs can als b dcd S abl 2.6 n pag 102 fr cn C(x) Sprng 2005 CS Inrn Chcks Algrh Vw ssag as a sqnc f 16-b ngrs; s sng 16-b ns-cpln arhc; ak ns-cpln f h rsl. _shr cks(_shr *bf, n cn) { rgsr _lng s = 0; whl (cn--) { s += *bf++; f (s & 0xFFFF0000) { /* carry ccrrd, s wrap arnd */ s &= 0xFFFF; s++; } } rrn ~(s & 0xFFFF); } Sprng 2005 CS Acknwldgns & s Sndr Fra Rcvr Sndr Fra Fra Rcvr Sp-and-Wa Sndr Rcvr (a) (c) Sndr Fra Fra (b) Rcvr Sndr Fra Fra (d) Rcvr Prbl: kpng h pp fll Exapl 1.5Mbps lnk x 45s R = 67.5Kb (8KB) 1KB fras pls 1/8h lnk lzan Sprng 2005 CS Sprng 2005 CS

5 Sldng Wndw Allw lpl sandng (n-d) fras Uppr bnd n n-d fras, calld wndw Sndr Rcvr SW: Sndr Assgn sqnc nbr ach fra (SqN) Manan hr sa varabls: snd wndw sz (SWS) las acknwldgn rcvd (LAR) las fra sn (LFS) Manan nvaran: LFS - LAR <= SWS LAR! SWS LFS Advanc LAR whn arrvs Bffr p SWS fras Sprng 2005 CS Sprng 2005 CS SW: Rcvr Manan hr sa varabls rcv wndw sz (RWS) largs fra accpabl (LFA) las fra rcvd (NFE) Manan nvaran: LFA - LFR <= RWS NFE! RWS Fra SqN arrvs: f LFR < SqN < = LFA accp f SqN < = LFR r SqN > LFA dscardd Snd clav s Sprng 2005 CS LFA Sqnc Nbr Spac SqN fld s fn; sqnc nbrs wrap arnd Sqnc nbr spac s b largr hn nbr f sandng fras SWS <= MaxSqN-1 s n sffcn spps 3-b SqN fld (0..7) SWS=RWS=7 sndr rans fras 0..6 arrv sccssflly, b s ls sndr rranss 0..6 rcvr xpcng 7, 0..5, b rcvs scnd ncarnan f 0..5 SWS < (MaxSqN+1)/2 s crrc rl Invly, SqN slds bwn w halvs f sqnc nbr spac Sprng 2005 CS

6 Cncrrn Lgcal Channls Mlplx 8 lgcal channls vr a sngl lnk Rn sp-and-wa n ach lgcal channl Manan hr sa bs pr channl channl bsy crrn sqnc nbr nx sqnc nbr n Hadr: 3-b channl n, 1-b sqnc n 4-bs al sa as sldng wndw prcl Sparas rlably fr rdr Sprng 2005 CS

10.5 Linear Viscoelasticity and the Laplace Transform

10.5 Linear Viscoelasticity and the Laplace Transform Scn.5.5 Lnar Vclacy and h Lalac ranfrm h Lalac ranfrm vry uful n cnrucng and analyng lnar vclac mdl..5. h Lalac ranfrm h frmula fr h Lalac ranfrm f h drvav f a funcn : L f f L f f f f f c..5. whr h ranfrm