CHAPTER 7

CONCLUSION

As an effort towards improving the performance of wireless networks, ATM

technology is incorporated with various quality enhancement protocols. The thesis

proposes four novel error control schemes for WATM networks to reduce CLR and

CDV. By proposing an effective call admission control scheme called Decentralised

CAC @CAC), the current work reduces end-to-end CTD as much as possible. This

results in the enhancement of the overall system quality of WATM networks.

The main results of this work are summasized below:

The performance analysis of Code combining ARQ reveals that the number of

retransmissions is reduced. It is also observed that shorter WATM cells reduce

CLR while employing retransmission. If retransmissions are not allowed, then

the use of standard cell can provide better performance. The performance of

Code combining ARQ is compared with Conventional A N . When conventional

ARQ is used, high throughput is obtained for shorter cell in a low SNR (< 6 dB)

environment. When Code combinirzg ARQ is used, there is only a little

difference in throughput for different cell lengths. On the other hand, in a large

S N R (> 6 dB) environment, both ARQ methods exhibit almost the same

throughput. The conclusion here is that Code combining ARQ is a preferable

technique due to its simplicity and robustness under fluctuating channel

conditions.

As an error control scheme, Code combining technique may not work efficiently

in a channel where there are bursty errors. Concatenated Early-Stop ARQ

scheme which is proposed in the second phase af the work performs well against

bursty errors. The throughput efficiency of the Early-Stop PLRQ protocol is

analyzed for different values of m and k, The analysis is also cam& out with and

without delay constraints. The simulation results have shown that the

Concatenated Early-Stop ARQ scheme can reduce the probability of cell

retransmission and maintain a higher throughput over a wider range of channel

error rates. While comparing with and without Early-Stop ARQ, it is infenred

that the throughput with Early-Stop ARQ is 49% higher than that of without

Early-Stop ARQ. Different forward error correction schemes such as Code

combining scheme, Convolutional coding, RS coding and Concatenated coding

are analyzed based on their bit error probability. From the results, it is found that

Concatenated Early-Stop ARQ is efficient among other forward error correction

schemes.

Early-Stop ARQ performs well in a noisy environment but it needs more

bandwidth allocation initially for sending redundant information, To overcome

this limitation, Rate Compatible Punctured Convolution (RCPC) codes can be

employed. Punctured convolution coding is an antactive idea since it could

dynamicaIly vary the coding rate, adapting to changing channel characteristics.

The performance analysis of RCPC codes and UEP are carried out and

simulation results are presented. For better throughput, the tixne-insensitive

services require HARQ scheme with longer packets while the time-sensitive

services use shorter packets. The RCPC coding scheme provides varying

retransmission packet size and code rate according to the channel condition and

improves the throughput efficiency. A tTEP code scheme using PCCs is found

suitable for WATM in which the cell header is protected by a relatively powerful

PCC to ensure correct delivery. Fox multimedia transmission, different source

data require different levels of error protection, UEP schemes are therefore

suitable for such applications.

To enhance reliability in WATM networks, many channel coding schemes such

as Code combining ARQ, -1y-Stop ARQ and RCPC codes have been used, To

get a better performance, Turbo coding is employed. The Turbo coded e m r

control mechanism using one bit quantized extrinsic information for WATM

networks has been presented. From the resuIts, it is confirmed that Turbo coding

provides considerable coding gains as well as better BER in the error prone

environment. From the simulation results, it is shown that BER of more than lu5

is achieved at an SNlR of 5 dl3 for the Quantized Turbo coding. With the

proposed Quantized Turbo scheme, memory requirements of Turbo decoders are

greatly reduced. The results confirm that the nonsystmatic Turbo coding

provides better BER in the error prone environment compared to other

techniques including systematic Turbo coding. It is amazing to obtain lo-' BER

at a very small SNR of (2.5 - 3) dE3 which is almost approaches wire line BER

performance in Nonsystematic Turbo codes. It can be concluded that Turbo

coding is a very promising technique to effectively control channel emrs for

wireless ATM networks under any situation.

* A combined hybrid ARQ error-control and scheduling scheme is presented for

wireless ATM networks. Instead of treating the error recovery and scheduling

scheme in separate DLC and MAC layers, the scheduling scheme is implemented

in conjunction with a retransmission scheme. With the aid of proper channel

modeling, type I1 hybrid ARQ is chosen as the error recovery scheme to combat

fading effects, while adaptive fairqueuing is used as the scheduling scheme to

achieve a fari. and efficient resource allocation. Simulation results show that the

proposed scheme can achieve a high throughput with minhnum delay and cell

loss rate.

The proposed Retransmission algorithms based on power priorities may be used

for the power control of retransmitted WATM cells. The: pedormance of an

RAW has been analysed and the simulation result shows that the throughput

achieved is greater in this scheme,

Simulation results illustrate a considerable improvement in the call admission

control and in the overall network performance of the proposed decentralised

CAC. A comparative analysis of decenrralised GAC with centralised CAC for

different measures, such as admission delays and throughput has been camed

out. It is concluded that the proposed DCAC scheme perfonns better than

centralised CAC.

The program codes used to obtain the results available in this thesis are enclosed in

Appendix A.

The investigations carried out in this work provide ample scope for doing hrther

research with regard to the following aspects:

The current work uses Coherent QPSK system as modulation technique. Higher

level modulation techniques like MSK, 4 -QAM, and 16-QAM schemes can also

be implemented for WATM.

As the current work shows good error performance for Turbo codes, Irregular

Turbo codes and Asymmetric Turbo codes may also be tried for better error

control.

The proposed QoS enhancement protocols may be tried in other wireless

networks like Adhoc networks, TCP/IP based networks, CDMA networks etc.

The proposed MAC protacols work on TDMA/TDD systems. These techniques

can be extended to other access techniques like CDMAIFDD, CDMA/TDD,

CDMAIOFDM, WCDMA etc.

The present work considers AWGN and Rayleigh fading channels only. Further

research can use other wireless channels like Ricean channel, Gilbert-Elliot

channel, etc.

APPENDIX A

Ilimulation Programs of Code Combining ARQ

I* Code Combining *I typedef struct bits

unsigned bits1 : 1 ; unsigned bits2 : 1; unsigned bits3 : 1; unsigned bits4 : 1 ; unsigned bits5 : 1; unsigned bits6 : 1 ; unsigned bits7 : 1; unsigned bits8 : 1; unsigned bits9 : 1; unsigned bits 10: 1 ;

)BITS;

BITS Strb, EnData;

void Decoder( BITS EnData, BITS Strb );

void Encoder( long int iData)

int icounter; long int iTempData; iTempData = iData;

Strb.bitsl0 iTempData Strb.bits9 iTempData Strb.bits8 iTempData Strb.bits7 iTempData Strb.bits6 iTempData Strb.bits5 iTempData Strb.bits4 iTempData Strb.bits3 iTempData Strb.bits2

= iTempData % 10; = iTempData.4 0; = iTempData % 10; = iTempDatdl0; = iTempData % 10; = iTempDatdl0; = iTempData % 10; = iTernpDatdl0; = iTempData % 10; = iTempDatall0; = iTempData % 10; = iTempDatdl0; = iTempData % 10; = iTempDataIl0; = iTempData % 10; = iTempData/ 1 0; = iTempData % 10;

/*Initial Data Display */ printf("\t\tCODE COMBINER\tV); printf("\n\t ****"********\t")- 3

printf("\nTransmitted Data:\tW); printf("l%ul',Strb.bitsl); printf("%u",Strb.bits2); printf("%uV,Strb.bits3); printf("%uW,Strb.bits4); printf("%u",Strb.bits5); printf("%u",Strb.bits6); printf("%u1',Strb.bits7); printf("%~"~Strb.bits8); printf("%u",Strb.bits9); printf("%ul\n",Strb.bitslO);

/* Encoded Data Display */ printf("\nEncoded Data:\t\tl'); printf("I%u",EnData.bits 1); printf("%u",EnData,bits2); printf("%u",EnData.bits3); printf("%u",EnData.bits4); printf(11%u",EnData.bits5); p~tf("%u",EnData.bits6); printf("%u",EnData.bits7); printf("%u",EnData.bits8); phtf("%u",EnData.bits9); printf("%uIW1,EnData.bits 10); Decoder( EEnData,Strb);

clc; format long nci = [ l 5 1 1 130305 22108415 28077687051; nci I = nci; foru= 1:1:3

pac l = 0; c = 1; nhecawgn = [f; g = 0; v = 0; s = o ; b = [I; tavg = [I; i f u - 1

k = 120; m = 40; n = 7 ;

elseif u - 2 k = 150; m = 100; n = 7;

elseif u == 3 k = 160; rn = 60; n = 7;

end for j = .0001:.0001:. 1

f = 0; for i = 0:1:4

pac(i+l) = nci(i+l) * (6) A i) * ((1 - j) A (5 11 - i)); pacl = pac(i4-I) + pacl;

end f m j =m:l:k

if (n- 1 > < (k-j) z = (n-1);

else z = (k-j);

end v = (factoria16- I )/((factorid(m- 1) * (factorial((j- 1)-(m- I)))))); g=pacl Am; s = (I-pacl) A 6-m); bQ)= z * v * g * s ; f = f + bfj);

end tavg = (rnlpac 1) t- fi nhecawgn(c) = (rn/tavg) * (443/5 1 1);

pac l = 0; c = c + l ;

end for x = 1:1:2

pac11 = 0; k l = 1; if x == 1

nl = 1; elseif x -2

nl = 7; end forj = .0001:.0001:.1

for i = 0: 1 :4 pacl(i+l) = ncil(i4-1) * ((j) A i) * ((I - J) A (5 1 1 - i)); pac11 = pacI(ii-1) + pacl I;

end ngbn(k1) = (pacl ll(pacl1 + (nl * (1 - pacll))) * (443151 1)); %disp(ngbn); pacll = 0; kl = kl + 1;

end i fx - 1

ngbn 1 = ngbn; elseif x = 2

ngbn7 = ngbn; end

end i f u = 1

nhecawgnl = nhecawgn; elseif u = 2

nhecawgri! = nhecawgn; efseif u = 3

nhecawgn3 = nhecawgn; end

end ber = .0001:.0001:.1; semilogx(ber,ngbnl ,':',ber,ngbn7,':',ber,nhecawgnl ,ber,nhecawgd,ber,nhecawgn3); axis([.0001 - 1 0 11); xlabelllBit enor rate'); ylabel(Throughput efficiency'); %grid on;

Simulation Programs of Concatenated Early-Stop ARQ

clc; format Iong nci = / 1 5 1 1 130305 22 1084 15 28077687051; nci 1 = nci; for u = 1:1:3

pac 1 = 0; c = 1; nhecawgn = [I; g = 0; v=o ; s = 0; b = [I; tavg = [I; i f u = 1

k = 150; m = 100; n=7;

elseif u = 2 k = 120; m = 60; n = 7;

elseif u -= 3 k = 120; m = 40; n = 7 ;

end for j = .0001:~0001:.1

f = 0; for i = 0:1:4

pac(i+l) = nci(i+l) * (6 ) * i) * ((1 - j) A (51 1 - i)); pacl = pac(i+l) -t pacl ;

end forj = m:I:k

if (11-11 < (k-j) z = (n-1);

else z = (k-j);

end v = (factorial@-l)/((factorial(m-1) * (factorial((j-1)-(m-1)))))); g = pacl A in; s = (1 -pacl) A 6-m); bu)= z * v * g * s ; f = f + b(j);

end

tavg = (m/pacl) + f; nhecawgn(c) = (dtavg) * (443/5 1 1); pacI = 0; c = c + l ;

end for x = 1:1:2

pac 1 1 = 0; k l = 1; i f x == 1

nl = 1; elseif x ==2

n l = 7; end for j = .0001:.0001:.1

for i = 0:1:4 pacl(i+l)=ncil(i+l) * (( j)Ai) * ((1 -j)*(511 - i)); pac11 = pacl(i+l) + pac11;

end ngbn(k1) = b a c l ll/acll + (nl * (1 - pacll))) * (443151 I)); %disp(ngbn); pac 1 1 = 0; k l = kl t- 1;

end i f x = 1

ngbnl = ngbn; elseif x = 2

ngbn7 = ngbn; end

end if u == 1

nhecawgnl= nhecawgn; elseif u = 2

nhecawgn2 = nhecawgn; elseif u = 3

nhecawgn3 = nhecawgn; end

end ber = .0001:.0001:.1; semilogx(ber,ngbn 1 ,':',ber,ngbn7,':',ber,nhecawgnl ,ber,nhecawgn2,ber,nhecaw~3); axis([.0001 . I 0 13); xlabel('Bit error rate'); ylabei(Throughput efficiency'); %grid on;

clc; p = 10; x i = [I; y2 = [I; x2 = [I; y2 = [I; x3 = [I; y3 = [I; x4 = [I; ~4 = El; x5 = [I; y5 = [I; %x6 = [I; %y6 = [I; Tors= 1:1:5

ifs== 1 m = 9 ; k = 10;

elseif s == 2 m = 45; k = 50;

elseif s == 3 m = 1; k = 1;

elseif s == 4 rn = 95; k = 100;

elseif s == 5 m = 100; k = 120;

end p = 10;

forr = 1:1:9 p = p110; ifp- 1

p m k = l ; else forj = 0:l:m-1

pmk = (factorial(k)/(factorialCj) * factorial(k - j)) * (1 - p) A j) * p A (k - j); end

end %disp(pmk); %disp(p); i f s= 1 x 1 (r) = p; y 1 (r) = pmk;

elseif s == 2 x2(r) = p; y2(r) = p d ;

elseif s == 3 x3(r) = p; y3(r) = p d ;

elseif s == 4 x4(r) = p; y4(r) = pmk;

eiseif s == 5 x5(rj = p; y5(r) = pmk;

end end %disp(y); %format long %disp(x); %disp(y); ioglog(x 1 ,y 1 ,x2,y2,x3,y3,x4,y4,x5,y5); xlabel('cel1-loss probability p'); ylabel('cel1-unrecovered probability p(m,k)'); %title(lprobability of decoding failure versus cell-error probability'); axis([le-8 1 le-12 11); legend('m=9 k= 10','m=45 k5Of,'rn= 1 k= l','m=95 k= 1 00','m= 100 k==120',2); end

clc; m = 45; k = 50; p = 10; %x = [I; %y = [I; f a r r= 1:1:9

p =p/iO; i f p = 1

pmk= 1; else forj = 0:l:m-1

prnk = (factorial(k)/(factorial(j) * factorial(k - j)) * (1 - p) A j) * p A (k - j); end end disp(pmk); dispb) ; x(r) = p;

y(r) = p d ; end %disp(y); %format long %disp(x); %disp(y); loglog(x,~); %axis([lOe-7 1 10e-12 11); grid on;

clc; format long nci = [ l 51 1 130305 22108415 28077687051; nci I = nci; foru = 1:1:3

pacl = 0; c = 1; nhecawgn = [I; g = o ; v = o ; s=o; b = [I; tavg = [I; i fu == 1

k = 120; m = 40; n = 1370;

elseif u = 2 k = 150; m = 100; n = 1370;

elseif u == 3 k = 120; m = 60; n = 1370;

end for j = -0001 :.0001:.1

f=O; for i = 0:1:4

pac(i+l) = nci(i-t.1) * (6) A i) * ((I - j) A (5 1 1 - i)); pacl = pac(i+l) + pacl;

end forj = m:l:k

if (n- 1) < (k-j) z = (n-1);

else

z = (k-j); end v = (factorial& l)/((factorial(m- 1 ) * (factorial(& 1 )-(m- 1 I))))); g = pacl Am; s = (I-pacl) A (j-m); b(j)= z * v * g * s ; f = f -t b(j);

end tavg = ( d p a c 1) + f; nhecawgn(c) = (m/tavg) * (443/5 1 1); pacl = 0; c = c + l ;

end for x = 1:1:2

pacl 1 = 0; k l = 1; i fx= 1

nl = 1; elseif x ==2

nl = 7; end forj = .0001:.0001:.1

for i = 0:1:4 pacl(i+l)= ncil(i+l) *(G) "i) * ( ( I - j) A (511 - i)); pacl 1 = pacl(i+l) + pac11;

end ngbn(k1) = @acl l/(pacll -I- (nl * (1 - pacl 1))) * (443511 1)); %disp(ngbn); pacll = 0; kl = kl -t 1;

end i f x = 1

ngbn 1 = ngbn; elseif x - 2

ngbn7 = ngbn; end

end if u == 1

nhacawgnl = nhecawgn; elseif u = 2

nhecawgn2 = nhecawgn; elseif u = 3

nhecawgn3 = nhecawgn; end

end her = .0001:.0001:,1;

sernilo~(ber,ngbn 1 ,':',ber,ngbn7,':?ber,nhecawgn I ,ber,nhecaw@,ber,nhecawgd); axis([.0001 .1 0 I]); xlabel('B1T ERROR RATE'); ylabel('THR0UGHPUT EFFICIENCY'); %grid on;

clc; p = 10; xl = [I; y2 = [I; x2 = [I; ~2 = El; x3 = [I; ~3 = [I; x4 = [I; ~4 = [I; x5 = [I; Y5 = [I; x6 = [I; ~6 = 11; for s = 1:1:6

i f s== 1 m = 9; k = 10;

elseif s == 2 m = 45; k = 50;

elseif s = 3 m = 1; k = 1;

elseif s == 4 rn = 95; k = 100;

elseif s = 5 m = 100; k= 120;

elseif s == 6 m = 100; k = 100;

end p = 10;

forr= 1:1:9 p = pll0; i fp= 1

pmk = 1;

else for j = 0:l:m-1

pmk = (factorial(k)/(factorial(j) * factorial(k - j)) * ( 1 - p) A j) * p A (k - j); end

end %disp@mk); %disp(p); i fs- 1

xl(r) = p; y 1 (r) = pmk;

elseif s == 2 x2(r) = p; y2(r) = pmk;

elseif s == 3 x3(r) = p; y3(r) = p d ;

elseif s == 4 x4(r) = p; y4(r) = pmk;

elseif s == 5 x5(r) = p; y5(r) = pmk;

elseif s == 6 x6(r) = p; YW = P&,

end end %disp( y); %fomat long %di sp(x); %disp(y); %axis([l Oe-7 1 10e- 12 11); ~oglog(x1 ,yl ,x2,y2,~3,y3,~4,~4,x5,y~,x6,1; axis([le-8 1 le-12 11); xlabel('ceI1-loss probability p'); ylabel('cel1-unrecovered probability p(m, k)'); title('probabi1ity of decoding failure versus cell-error probability'); %grid on; %legend('m=g k= 1 Ot,'m=45 k=50','m= 1 k=1 ','m=95 k=1 OO','m=100 k 120','m=I 00 k=1 O0',4); End ,

clc; n = 2024; format long x = [I;

e = -001; for i = 1:1:6

i f i - I x(i) = e;

else x(i} = x(i- l)/l 0;

end end disp(x); pu = [I; qu = [I; forif 1:1:6

pu(i) = ( 1 - x(i)) " 2024; qu(i) = ( I - pu(i));

end dispbu); disp(qu); pd = pu; qd = qu; for i = 1:1:6

m(i) = pu(i) * pd(i); b(i) = pd(i) * qu(i); k(i) = (pd(i) * qu(i)) A 2; j(i) = pu(i) * qu(i) * pd(i) * qd(i); g(i) = ((k(i) + j(i) + k(i))/(b(i) + b(i)) * 64); n(i) = (m(i)/(m(i)+g(i)));

end disp(n); serniIogx(x,n); xlabel('BIT ERROR RATE'); YLABEL('THR0UGHPUT'); %grid on;

clc; n = 2024; format long x = 0 ; e = .01; fori = 1:1:7

i f i - 1 x(i) = e;

else x(i) = x(i-l)/lO;

end

end disp(x); pu = tl; pd = 11; for i = 1:1:7

pu(i) = ( 1 - x(i)) A 2024; end disp(pu); pd = pu;

= 11; I- = [I; nc = [I; fori = 1:1:7

m(i) = pu(i)"2; r(i) = m(i) t- (1 - m(i)) * 128; nc(i) = m(i)/r(i);

end disp(nc); %semilogx(x,nc); for i = 1:1:7

j(i) = pu(i) * (pu(i) A 10); k(i) = j(i) + ( I - j(i)) * 128; nc 1 O(i) = j(i)/k[i);

end semiIogx(x,nc,x,nc 1 0); grid on;

Simulation Programs of RCPC coding

Pb = [I; sopt = [I; for x =1:100000

tempPb = 1 /(2*x); te~npSopt = 16 * (sqrt(3 -(. 125/log(l -tempPb)))- I); Sopt = [Sopt tempsopt]; Pb = [Pb tempPb];

end semi10gx(?b,Sopt7'm1j; xlabel('Channe1 BER'); ylabel('Blocksize(Bits)');

clc; tempa = 1; tempc =I ; throav = [I; PC = [I; ber = (];b6=[]; throu-arq = [I; berl = [I; PC = 0; Pb = 0; k=[l 2 3 4 51; l(k) = [ l 2 4 8 161;

d l =[3 4 5 6 7 81; Cdl = [24 740 13321 217761 33 15491 482781771;

for x = 1:5000, X

pb = 1/(2*x);

berl = [ber? pb];

prd = I-( 1 8 4 ; -pb)"3

lav 1 = 460/(1 -prd);

tav 1 = 384/lav 1 ;

throu-arq = 1 ) ; [thou-arq tav

tempa = pc(l)*pc(2)*pc(3)*pc(4)*pc(5);

a = 16 * tempa; a bl = 0; b2 = 0; b3 = 0; b4 = 0; b5 = 0;

for k=1:5,

elseif k == 3

else

end end

tav = 7.3/(8+lav);

throav = [throav tav 1;

ber = [ber pb];

end

semilogx (ber, throav,'b-.',berl ,throu-arq,'mf); xlabel('BERf); ylabel('THROUGHPUTf); legend('Hybrid ARQ(RCPC)','ARQf) title('Cornparison of throughput of Hybrid ARQ with Simple ARQ Technique for Block size 3 84 bitsf);

output 1 = ClossR(d 1 ,Cdl ,totalR(l));

ber 1 = output 1 (1 ,:); cIrl = output1 (2,:);

logIog(ber1 ,clrl , ' b - - ' , b e r 2 , c l r 2 , ' g * ' , b e r 3 , c k 3 , ' r . ' , b ~ ' ) ; legend('8/24','8/16','8/ 12','8/1 01,'8/91; xlabel('l3ER'); y1abel('CLR1); title('Accepted CLR with 5 rates for block size 48 bits');

hnction out - throughput(d,Cd,pb) PC = 0;

for i=1:6 Pd = 0.5 * (pb)"d(i);

tempPc = Pd * Cd(i); pc = pc t tempPc;

end tempBer = pc/8; pc = I - ( I - tempBer)/\384; out = pc;

function out = ClossR(d,Cd,R)

Clr = [I; Ber = [I; PC = 0; for x= 1 : 10000

Pb = 1/(2*x); for i=1:1:6

Pd = 0.5 * (PbIAd(i); tempPc = Pd * Cd(i); PC = PC I- tempPc;

end tempBer = Pc/8; tempClr = 1 - (1 - tempBer)"48; Clr = [Clr tempClr]; Ber = [Ber Pb]; PC = 0;

end out = [Ber ; Clr]; Ber Clr

dl = [ I 4 15 16 17 18 191; Cdl = [8 0 160 0 424 01;

output 1 = ClossR(d 1 ,Cdl,totalR(l));

berl = outputl(1,:); clrl = output 1 (2,:);

loglog(ber 1 ,clr 1 ,%--',ber2,clr2,'gw,ber3,clr3,'r.',ber4,c~4,'c+t,ber5,clr5,'mt); legend('8/24','8/16','8/ 12','8/10','8/9'); xlabel('BER'); ylabel('CLR'); title('Accepted CLR with 5 rates for block size 48 bits');

Simulation Programs of Turbo Coding

clc; clear all; clear all; % Choose decoding algorithm fprintf('\n O=SOVA \n 1 =logemap'); dec-aIg = input('\n choose the decoding aIgorithm from the choiser); if isempt y(dec-alg)

dec-alg = 0; end

totallength = input('Enter the Size of the ATM packets'); if isempty(total1ength)

totallength = 56; end

g = [ 1 1 1;l 0 11; [n,K] = size(g); m = K - 1; nstates = 2"m;

puncture = input(' Please choose punctured / unpunctured (0/1): default 0 '1; if isempt puncture)

puncture = 0; end

rate = 1 /(2+puncture);

niter = input(7n Enter number of iterations I); if isempty(niter)

niter = 10; end

% Number of frame errors to stop criterior ferrlirn = input('h Enter the number of frames in errors to terminate '); if isempty(ferr1im)

ferrlim = 3; end

%% For get the signal to noise ratio values ~bNOdb = input(' \n Enter the the SNR (Eb/NO) in d~ l);

if isempty(EbN0db) EbNOdb = [5.0];

end

for i = 1:n for j = 1:K

fprintf( '%6d', g(i j)); end fpIintf('W);

end

for i = 1 :length(EbNOdb) @rintf('% 10.2f ,EbNOdb(i));

end

% convert signal to noise ratio from dB to the normal value for nEN = l:length(EbNOdb)

normal = (EbNOdb(nEN)/ 1 0); en = 1 OA(normal) L-c = 4*s*en*rate; sigma = l/sqrt(2*rate*en);

% Clear bit error counter and frame error counter errs(nEN, I :niter) = zeros(1 ,niter); nferr(nEN, 1 :niter) - zeros(1 ,niter);

nframe = 0; % clear counter of transmitted frames while nferr(nEN, niter)<ferrlim

nfiame = nfxarne + 1 ; x = round(rand(1, totallength-m)); % info. bits [temp, alpha] = sort(rand(1 ,totallength)); % random interleaver mapping en-output = en-coder( x, g, alpha, puncture ) ; % encoder output (+I/- I)

r = en~output+sigma*randn(l,totallengtlP(2+pcre)); % received bits yk = demux(r,alpha,puncture); % demux to get input far decoder 1 and 2

% Initialize extrinsic information L-e(l :totallength) = zeros(1 ,totallength);

for iter = 1 :niter

% Decoder one L_a(alpha) = L-e; % a priori info. if dec-alg -- 0

L-all= logmapo(rec-s(l,:), g, L-a, I); % complete info. else

L-all= sova-algo(rec-s(l,:), g, L-a, 1); % complete info. end

L-e = L-all - 2*rec-s(lyl:2:2*totallength) - L-a; % extrinsic info.

% Decoder two L-a = L-e(a1pha); % a priori info. if dec-alg = 0

L-all= logrnapo(rec-~(2,:)~ g, L-a, 2); % complete info. else

L-all= sova-algo(rec-~(2,:)~ g, L-a, 2); % complete info. end L-e = L-all - 2*rec-s(2,1:2:2*totallength) - L-a; % extrinsic info.

% Estimate the info. bits xhat(a1pha) = (sign(L-all)+ 1)M;

% Number of bit errors in current iteration

% Count fi-arne errors for the current iteration if err(iter)> 10

nferr(nEN,iter) = nferr(nEN,iter)+ 1 ; end

end

% Total number of bit errors for all iterations errs(nEN, 1 :niter) = errs(nEN,l :niter) + err(1 :niter);

if rern(nfi-ame,3)==0 I nferr(nEN, niter)=fedim % Bit error rate

ber(nEN, 1 :niter) = errs(nEN, 1 :niter)/nframe/(totallength-m); % Frame error rate

fer(nEN, 1 :niter) = nferr(nEN, 1 :niter)/nfrme;

% Display intermediate results in process @rintf('**"*"******** Eb/NO = %5.2f db **************\n' EbNOdb(nEN))- fprintf('Frame size = %d, rate 1/%d. W, totallength, 2+puncture); fprintf('%d frames transmitted, %d frames in error.\nl, nframe, nferr(nEn, niter));

fprintf('Bit Error Rate (fi-om iteration 1 to iteration %d):\nt, niter); for i=l:niter

@rintf('%8,4e ', ber(nEN,i)); end fprintf('\nf); f+printf('Frarne Error Rate (from iteration 1 to iteration %d):\nf, niter); for i= 1 :niter

fprintf('%8.4e ', fer(nEN,i)); end fprintf('\n '); fpr&f('*********' 1;

end end

end

Eunction en-output = en-coder( x, g, alpha, puncture ) [n,K] = size(g); m = ( K ) - 1; L-info = length(x); totallength = L-info + m; % For the 1 st RSC coder, generating corresponding codeword input = x; output 1 = RSC(g,input, 1); y(1,:) = outputl (1 :2:2*totallength); y(2,:) = outputl (2:2:2*totallength); % interleaver input to second encoder for i = 1 :totallength

input1 (1 ,i) = y( 1 ,alpha@)); end output2 = RSC(g, input l(1,l :totallength), -1 ); y(3,:) = output2(2:2:2*totallength);

if puncture > 0 for i = 1 :L_total

forj = 1:3 en_output(l,3 *(i-l)+j) = y(j,i);

end end

else for i= 1 :totallength

m-output(1 ,n*(i- 1)+ 1) = y( 1 ,i); if rem(i,2) % odd check bits from RSC1

en-output(1 ,n*i) = y(2,i);

eIse % even check bits from RSC2

en-output(1 ,n*i) = y(3,i); end

end end

en-output = 2 * en-output - ones(size(en-output));

clc; clear all; t=cputime;

for sn1==0:5 hata(snr+ l)=O;

for j=l :carpan(snr+l) n= 100; u=randint(l ,n-2); u(n)=O; kafes=poly2trellis(3 ,[5 73); v=convenc(u,kafes); for i=1:2*n

s(i)=2*v(i)- 1 ; end r = awgn(s,snr,'measured');

x l l 1=-1;xl12=-1;x121=1;x122=1; x23 1 =- 1 ;x232=1;x241=1 ;x242=-1; x311=1;x312=1;x321=-l;x322=-1; x43 1 = 1 ;x432=-1 ;x441=- 1 ;x442=1;

k=O; Eb=2;NO=~b/(l OA(snr/l O));sigma=NO/2; for i=1:2:2*n

k=k-t- 1 ; gama 1 1 (k)=exp((-(r(i)-x 1 1 1)"Z-(r(i4- 1 )-x 1 1 2)A2)/2/sigrma); gama 12(k)=exp((-(r(i)-x 12 1 )"2-(r(i+l )-x 122)"2)/2/sigma); gama23(k)=exp((-(r(i)-x23 1 )"2-(r(i+ 1)-x232)"2)/2/sigma);

gama24(k)=exp((-(r(i)-x24 1 )"2-(r(i+ 1)-x242)/'2)/2/sigma); gama3 1 (k)=exp((-(r(i)-x3 t I)"2-(r(i+l)-x3 12)"2)/2/siglna); gama32(k)=exp((-(r(i)-x321)"2-(r(i+1)-~322)*2)/2/si~a); gama43(k)=exp((-(r(i)-x43 1)A2-(r(i+1)-x432)A2)/2!sigma); gama44(k)=exp((-(r(i j-x44 1 )"2-(r(i+ 1)-x442)*2)/2!sigma);

end

alfal (l)=gamal 1 (l);affa2(1)=gamal2(1);alfa3(l)=O;alfa4(1)=0; for i=2:n

alfa 1 (i)=alfal (i- 1 )*gama 1 1 (i)+alfa3(i- 1 j*garna3 1 (i); alfa2(i)=alfal (i- 1 )*gama lZ(i)+alfa3(i- l)*gama32(i); alfa3 (i)=alfaZ(i- 1 ) *gama23 (i)+alfa4(i- 1 )*gama43(i); alfa4(i)=alfa2(i- 1 )*gama24(i)+alfa4(i- 1 )*gama44(i);

end

betal (n-l)=gamal 1 (n);beta3(n-l)=gama3 l(n);beta2(n- l)=O;beta4(n- 1)=0; for i=n-2:- 1 : 1

betal (i)=betal (i-t l)*gainal l(i+l)+beta2(i+l)*gama12(i+l); beta2(i)=beta3(i+ l)*gama23(i+l )+beta4(i+l)*gama24(i+ 1); beta3(i)=betal (ii- l)*gama3 l(i+l)+beta2(i+l)*gama32(i+l); beta4(i)=beta3(i+ l)*gama43(i+l)+beta4(i+l)*gama44(i+l);

end

for i=2:n-2 pay=(alfal (i- l)*gamal I(i)*betal (i)+alfa2(i-l)*gama23(i)"beta3(i)+ ...

alfa3(i- l)*gama3 1 (i)*beta 1 (i)+alfa4(i-l)*garna43(i)*beta3 (i)); payda=(alfal (i- l)*gamal2(i)*beta2(i)+alfa2(i- l)*gama24(i)*beta4(i)+-..

alfa3(i- l)*gama32(i)*beta2(i)+alfa4(i- l)*gama44(i)*beta4(i)); L-a(i)=log(pay/payda);

end for i= 1 :n-2

if L-a(i)>O a(i)=O;

else a(;>= 1 ;

end end a(n)=O; hata(snr+ 1 )=hata(snr+ 1 )+sum(abs(u-a));

end hata(snr+ 1); bit-hata-orani(snr+l )=hata(snr+l)/100/carpan(~nr+ I )

end snr=O: 5:25; semilogy(snr,bit-hata-orani), title('MAP1);x1abel('Eb/NO(dB)');ylabel('Bit Error Rate'); zaman=cputime- t

function L-all= sova(rec-s, g, L-a, ind-dec)

totallength = length(L-a); [n,K] = size(g); m = K - 1; nstates = 2"rn; Lifty = 1 el 0;

delta = 30;

% Set up the trellis defined by g. [next-out, next-state, last-out, last-state] = trellis(g);

% Initialize path metrics to -1nfiy for t==l :totallength+l

for state=l :nstates path-rnetric(state,t) = -hfty;

end end

% Trace forward to compute all the path metrics path-metric(1,l) = 0; for t= 1 :totallength

y = rec-s(2*t-l:2*t); for state=l :nstates

symO = last-out(state, 1 :2); syrnl = last_out(state,3:4); state0 = last-state(state, 1); state1 = last_state(state,2); MkO = y*symOf - L_a(t)/2 t path-metric(state0,t); Mkl = yXsyml' + L_a(t)/2 + path_metric(statel ,t);

if MkOsMk1 path-metric(state,t+l )=MkO; Mdiff(state,t+ 1) = MkO - Mkl ; prev-bit(state, t+l) = 0;

else path-metric(state,t+ l)=Mkl ; Mdiff(state,t+l) = Mkl - MkO; prev-bit(state,t+l) = 1 ;

end

end end

% For decoder 1, trace back from all zero state, & for decoder two, trace back from the most likely state if ind-dec == 1

mlstate(totallength+l) = 1 ; else

mlstate(totallength+ 1) = find( pathmetric(: ,totallength+l)==max(path~metrie(:,totalltength+ 1)) ); end

% Trace back to get the estimated bits, and the most likely path for t=totallength:-1 : 1

est(t) = prev-bit(mlstate(t+l),t+l); mlstate(t) = last-state(mlstate(t+l), est(t)+l);

end

% Find the minimum delta that corresponds to a compitition path with different info. bit estimation. & Give the soft output for t=l :totallength

Ilr = Infty; for i=O:delta

if t-ti<totallength+l bit = 1 -est(t+i); temp-state = last-state(mlstate(t+i+l), bit+l); for j=i-1 :-1:0

bit = prev-bit(temp-state,t+j+l); temp-state = last-state(temp-state, bit+l);

end if bit-=est(t)

llr = min( lk,Mdiff(mlstate(t+i+l), t+i+l) ); end

end end L-all(t) = (2*est(t) - 1) * llr;

end

function L-all= logmapo(rec-s,g,L-a,ind_dec)

L-total = length(rec-s)/2; [n,K] = size(g); m = K - I ; nstates = 2"m;

% Set up the trellis [next-out, next-state, last-out, last-state] = treIlis(g); Infty = le10;

% Initialization of Alpha Alpha(1, I ) = 0; Alpha( 1,2:nstates) = -Lnfty*ones(l ,nstates- 1);

% Initialization of Beta if ind-dec== 1

Beta(L-total, 1) = 0; Beta(L-total,2:nstates) = -Infiy*ones(l ,nstates-1);

elseif ind-dec==2 Beta(L-total, 1 :nstates) = zeros(1 ,nstates);

else @rintf('ind-dec is limited to 1 and 2!\n');

end

% Trace forward, compute Alpha for k = 2:L_total+ 1

for state2 = 1 :nstates gamma = -hfty*ones(l ,nstates); garnma(1ast-state(stat e2, I)) = (-rec-s(2* k-3)+rec-s(2 *k-2)*1ast__out(state2,2)).. ..

-log( 1 +exp(L-a(k- 1))); gamma(1ast-state(state2,2)) = (rec-s(2*k-3)+rec-s(2*k-2)*last_out(state2,4)). . ..

+L-a(k- 1 )-log( 1 +exp(L-a(k- 1)));

if(sum(exp(gamma+Alpha(k- 1 ,:)))< 1 e-300) Alpha(k,state2)=-Infty;

else Alpha(k,state2) = log( sum( exp( gamma+Alpha(k-1,:) ) ) );

end end temprnax(k) = rnax(Alpha(k,:)); Alpha(k,:) = Alpha(k,:) - tempmax(k);

end

% Trace backward, compute Beta

for k = L-total- I :- 1 : 1 for state1 = 1:nstates

gamma = -Infty*ones( 1 ,nstates); gamma(next-state(statel,l)) = (-rec-s(2*k+ l)+rec-s(2 *k+2)*nextout(state 1,~)). ...

-log( 1 +exp(L-a(k+ 1 ))); gamma(next_state(statel,2)) = (rec-s(2*k+ l )+rec-s(2*k+2)*next_out(state l,4)) ....

+L-a(k+ 1 )-log( 1 +exp(L-a(k+ 1 ))); if(sum(exp(gamma+Beta(k+1,:)))< 1 e-300)

Beta(k,state I)=-Infty; else

Beta(k,state 1) = log(sum(exp(gamma+Beta(k+ 1 ,:)))); end

end Beta(k,:) = Beta(k,:) - tempmax(k+l);

end

% Compute the soft output, log-likelihood ratio of symbols in the frame for k = 1 :L-total for state2 = 1 :nstates

gamma0 = (-rec-s(2*k- l)+rec~~(2*k)*last~out(state2~2))~. .. -log( 1 +exp(L-a(k)));

gamma1 = (rec~s(2*k-l)+rec~s(2*k)*last~out(state2,4)) ... +L-a$)-log(l+exp(L-a(k)));

tempO(state2) = exp(gamma0 + Alpha(k,last_state(state2,1)) t- Beta(k,state2)); temp1 (state2) = exp(gamma1 3. Alpha(k,last_state(state2,2)) + Beta(k,state2));

end L-all(k) = log(sum(temp1)) - log(surn(temp0));

End

clc ; clear all; clear all; % Choose decoding algorithm fprintf('\n O=QSOVA 'm 1-Qrnap'); dec-alg = input('\n choose the decoding algorithm from the choise'); if isempty(dec-alg)

dec-alg = 0; end

% size of the ATM Frames totallength = input('Enter the Size of the ATM packets'); if isempty(total1ength)

totallength = 56; end

[n,K] = size(g); m = K - 1; nstates = 2"m;

puncture = input(' Please choose punctured 1 unpunctured (04): default 0 I);

if isempty(puncture) puncture = 0;

end

% Code rate rate = I /(2+punchlre);

% Number of iterations

niter = input('~1 Enter number of iterations I); if isempty(niter)

niter = 10; end

% Number of frame errors to stop criterior ferrlim = input('\n Enter the number of frames in errors to terminate I); if isempty(ferr1im)

ferrlim = 3; end %% For get the signal to noise ratio values EbNOdb = input(' \n Enter the the SNR (Eb/NO) in dB '1; if isempty(EbN0db)

EbNOdb = E5.01; end

for i = l:n for j = 1:K

Qrintf( '%6d1, g(i j)); end fprintf('\nl);

end

for i = 1 :length(EbNOdb) fprintf('% 1 0.2f ,EblOdb(i));

end

% convert signal to noise ratio from dB to the normal value for nEN = 1 :length(EbNOdb)

normal = (EbNOdb(nEN)/ 1 0); en = 1 OA(normal) L-c = 4*s*en*rate; sigma = l/sqrt(2*rate*en);

% Clear bit error counter and frame error counter errs(nEN, 1 :niter) = zeros(1 ,niter); nferr(nEN, 1 :niter) = zeros( 1 ,niter);

nframe = 0; while nferr(nEN, niter)<fenrlim

nframe = nframe + 1; x = round(rand(1, totallength-m)); [temp, alpha] = sort(rand(1 ,totallength)); en-output = en-coder( x, g, alpha, puncture ) ;

% Initialize extrinsic information L-e(1 :totallength) = zeros(1 ,totallength);

for iter = 1:niter

% Decoder one L-a(alpha) = L-e; % a priori info.

L-a 1 = quantiz(L-a(alpha),-4: 1 :3 ,-4A 5); % if dec-alg = 0

L-all= logmapo(rec-s(l,:), g, L-a, 1); % complete info. else

L-all= sova-algo(rec-s(l,:), g, L-a, 1); % complete info. end

L-e = L-all - 2*rec_s(l, 1 :2:2*totaIlength) - L-a; % extrinsic info.

% Decoder two L-a = L-e(a1pha); % a priori info.

L+a2= L-a .' ; % L-a2 = quantiz(L-a,-4: 1 :3,-4: 1 5); % if dec-alg = 0

L-all= logmapo(rec-s(2,:), g, L-a, 2); % complete info. else

L-all = sova-algo(rec-s(2,:), g, L-a, 2); % complete info. end L-e = L-all - 2*rec-s(2,1:2:2*totallength) - L-a; % extrinsic info.

% Estimate the info. bits

% Number of bit errors in current iteration

% Count frame errors for the current iteration if err(iter)> 10

nferr(nEN,iter) = nferr(nEiN,iter)+ 1 ; end

end

% Total number of bit errors for all iterations errs(nEN, 1 :niter) = errs(nEN, I :niter) + err(1 :niter);

if rem(nframe,3)==0 I nferr(nEN, niter)=ferrlim % Bit error rate

ber(nEN, 1 :niter) = errs(nEN, 1 :niter)/nframe/(totallength-m); % Frame error rate

fer(nEiN, 1 :niter) = nferr(nEN, 1 :niter)/nframe;

% Display intermediate results in process fpfintf('**********-Xd** Eb/NO = OA5+2f db **************hi, ]EbN&jb(nEN)); fprintf('Frame size = %d, rate l/%d. W, totallength, 2tpuncture); fprintf('0hd frames transmitted, %d frames in ermr.W, nframe, nferr(nEN, niter)); fhrintf('Bit Error Rate (fiom iteration 1 to iteration %d):\nt, niter); for i= 1 :niter

+rintf('%8.4e ', ber(nEN,i)); ' end

fbrintf('\nl); fprintf('Frame Error Rate (from iteration 1 to iteration %d):\n', niter); for i=l :niter

@rintf('%8.4e ', fer(nEN,i)); end fprintf('\nf); fpSntf(f*********t >;

end end

end

clc; clear all; t=cputime;

for snr=0:5 hata(snr+i )=0;

for j=l:carpan(snr+l) n= 100; u=randint( 141-2); u(n)=q kafes=poly2trellis(3,[5 73); v=convenc(u,kafes); for i=l:2*n

s(i)=2*v(i)- 1 ; end r = awgn(s,snl;'measuredl);

k=O ; Eb=2;NO=Eb/(l OA(snr/ 1 O));sigma=N0/2; for i=1:2r2*n

k=k+ 1 ; gama 1 1 (k)=exp((-(r(i)-x 1 1 1)"2-(r(i+ 1 )-x 1 1 2jA2)/2/sigma); gama 1 2(k)=exp((-(r(i)-x 12 1)A2-(r(i+1)-x 122)"2)/2/sigma); gama23 (k)=exp((-(r(i)-x23 1)"2-(r(i+l )-x232)"2)/2/sigma); gama24(k}=exp((-(r(i)-x24 l)"2-(r(i+ 1 )-x242)"2)/2/sigma); gama3 1 (k)=exp((-(r(i)-x3 1 1)"2-(r(i+l )-x3 1 2)fi2)/2/sigma); garna32(k)=exp((-(r(i)-x32 1)A2-(r(i+l)-x322)A2)/2/sigma);

gama43(k)=exp((-(r(i)-x43 1 )"2-(r(i+ 1 )-x432)^2)/2/sigma); gama44(k)=exp((-(r(i)-x44 ! )"2-(r(i+ 1 )-x442)"2)/2/slgma);

end

aIfal(1 )=gamal 1 (l);alfa2(1)=gamal2(I);alfa3(1)=0;alfa4(1)=0; for i=2:n

alfal (i)=alfa l (i- 1 )*gamal 1 (i)+alfa3(i- l)*gama3 1 (i); alfa2(i)=alfal(i- l)*gamal2(i)+alfa3(i-l)*gama32(i); alfa3 (i)=alfa2(i- 1 )*gama23(i)+alfa4(i- l)*gama43(i); alfa4(i)=alfa2(3- l)*gma24(i)+alfa4(i- i { i ) ;

end

beta 1 (n- l)=garnai I (n);beta3(n- l)=gama3 l (n);beta2(n- l)=O;beta4(n- l)=0; for i=n-2:- 1 : 1

beta1 (i)=beta 1 (i+ 1 )*gamal 1 (i+ I)+beta2(i+ 1 )*gama 12(i+ 1); beta2(i)=beta3(i+l)*gama23(i+ l)+beta4(i+ l)*garna24(i+l); beta3(i)=betal (i+l)*gama3 1 (i+l)+beta2(i+l)*gama32(i+l); beta4(i)=beta3(i+ 1 )*garna43(i+ l)+beta4(i+ l)*gama44(i+ 1 );

end

for i=2:n-2 pay=(alfal (i-l)*gamaI 1 (i)*betal(i)+alfa2(i-l)*gama23(i)*beta3(i)+ ...

alfa3(i- l)*gama3 1 (i)*betal (i)+alfa4(i- l)*gama43(i)*beta3(i)); payda=(alfal (i- l)*gamal2(i)*beta2(i)+alfa2(i- l)*garna24(i)*beta4(i)+.

alfa3(i- l)*gama32(i)*beta2(i)+alfa4(i- l)*gama#(i)*beta4(i)); L-a(i)=logO,ay/payda);

end for i= 1 :n-2

if L-a(i)>O a(i)=O;

else a(i)= 1 ;

end end a(n)=O; hata(snrtl)=hata(snr+ 1 )+sum(abs(u-a));

end hata(snrt 1); bit-hata-orani(s&l)=hata(snrt-1)/1 OO/carpan(snr+ 1 )

end sni=0:5:25; semilogy(snr,bit-hata-orani), title(vMAP');xlabeI('Eb/NO(dB)');ylabel'Bit Error Rate'); zaman=cputime-t

function L-all= sova(rec-s, g, L-a, ind-dec)

totallength = length(L-a); [n,K] = size(g); m = K - 1; nstates = 2"m; infiy = 1 el 0;

% Set up the trellis defured by g. [next-out, next-state, last-out, last-state] = tre!lis(g);

% Initialize path rnetrics to -1nfty for t= 1 :totallength+ 1

for state= 1 :nstates path-rnetric(state,t) = -Infty;

end end

% Trace forward to compute all the path metrics path-metric(1 , 1 ) = 0; for @= 1 :totallength

y = rec-s(2*t-l:2*t); for state=l :nstates

symO = last-out(state, 1 :2); syml = last-out(state,3:4); state0 = last-state(state, 1); state1 = last_state(state,2); MkO = y*sym0' - L-a(t)/2 + path-metric(state0,t); Mkl = y*symlt 3 L-a(t)/2 + path-rnetric(state1 ,t);

if MkO>Mkl path-metric(state,t+ l)=MkO; Mdiff(state,t+l) = MkO - Mkl; prev-bit(state, t+ 1) = 0;

else path-metxic(state,t+l)=MStl ;

Mdiff(state,t+ 1 ) = Mk 1 - MkO; prev-bit(state,t+l) = 1 ;

end

end end

% For decoder 1, trace back fi-om all zero state, & for decoder two, trace back from the most likely state if ind-dec = 1

mlstate(totallength+1) = 1 ; else

mlstate(totallength+l) = find( path-metric(:,totallength+ l)==maxCpath~metricf:,totallength+~)) ); end

% Trace back to get the estimated bits, and the most likely path for t=totallength:- 1 : 1

est(t) = prev-bit(mlstate(t+l),t+l); mlstate(t) = last-state(mlstate(t+l), est(t)+l);

end

% Find the minimu111 delta that corresponds to a cornpitition path with different info. bit estimation. & Give the soft output for e l :totallength

llr = Infty; for i=O:delta

if t+i<tatallength-t-1 bit = 1 -est(t+i); temp-state = last-state(mlstate(t+i+ I), bit+l); for j=i-1 :-1 :O

bit = prev-bit(temp-state,t+j+l); temp-state = last-state(temp-state, bit+l);

end if bit-=est(t)

Ilr = rnin( llr,Mdiff(mlstate(t+i+ I), t+i+ 1) ); end

end end L-all(t) = (2*est(t) - 1) * llr;

end

Simulation Programs of Combined Hybrid ARQ and Adaptive Scheduling

c1c;clear all; PsO= 1 -( 1 -0.0 1 65)."8; PSI=] -(I-4.88*10."-8)."8; PO=O.O952;P 1=0.9048;z= 1 ;xl=O;x2=0; for n=79:-155

kbn(z)=55/n; j 1 =floor((2*n)-55/2)+1; j2=floor(n-55/2)+ 1 ;

for j=fix(j2):n %comb 1 (j)=factorial(n)/(factorial(j)*factorial(n-j)); x l=x l+(factorial(n)/(factoria1~)*factorial(n-j))*P~O.~j*(l -PsO).*(n-j));

end % Prl=Pr2=xl for k=fixCj 1):2*n % comb2=factorial(2*n)/(factorialO')"facto~al(2*n-j)); c = f a c t o r i a l ( 2 * n ) / ( f a c t o r i a l ( k ) * f a c t o ~ k * ( l -PsO)./'(n-k);

x2=x2+c; end % Pr3=x2 Ets(z)=( 1 +x l+(x 1 *x 1 *x2)-(x 1 *x 1 *(x2-"2)))/(1 -(x 1 ."2)*(x2."2)); NO(z)=( 1 /Ets(z))*(55/n); z=z+ 1 ; end yl=Pl(n); % - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - q=1 ;x3=0;x4=0; for nl=79:-1:55 for l=fix(j2):nl % comb3=factorial(n 1 )/(factorial(j)* factorial(n 1 -j)); x3=x3+factorial(nl)/(factorial(l)*factorial(nl-1))*Psl ."l*(l-Ps l)."(nl-1);

end y2=p2(n); % Pr 1 =Pr2=x3 for rn=fix(j l):2 *n 1 % comb4=factorial(2*nl)/(factorialO')"facto~al(2*nl-j));

x4=x4+factorial(2*n l)/(factorial(m)*factoriaI(2*n 1 -m))*Ps I .%*( 1 -Ps 1 )."(n 1 -m); end y373(n); % Pr3=x4 Etsl (q)=( 1 +x3-tx3*x3 *x4-x3*x3 *~4.~2)/(1 -x3 ."2*~4."2); N 1 (q)=( 1 /Ets(q))*(SS/n 1 ); q=q+ 1 ; end

N=O; for t= 1 : length(Ets)

N(t)=PO*NO(t)+P I *N 1 (I); end % Ien=length(N); x=0.625:.025:0.85 plot(x,yl ,'-',x,y2,'-*',x,y3,'--'); Iegend('type-I hybrid ARQq,'type-Il hybrid ARQ','type-I1 hybrid ARQ&adaptive fair-queueing'); %subplot(3,172);p10t(x,y2,'--');legend('type-I1 hybrid ARQ') %subplot(3,1 ,3);plot(x7y3,'-"');Iegmd('type-I1 hybrid ARQ&adaptive fair-queueing'); xlabel(Traffic Load'); ylabel('avg. delay of UBR traffic (ms)');

%ERROR CONTROL IN WIRELESS ATM % %CODING RATE Vs AVERAGE DELAY k=input('enter the number of info. bytes'); n=55: 79; e0=0.0165; e1=1.88* loA(-8); psO=O. 124; psl=0.0000003 9; pr03=0; for i=99.5: 126 f;03=(prod(l:(2*n))./(prod(l :i).*prod( 1 :(2*n-i)))).*(psO."i)."(ll-ps0).*(2*n-i)); pr03=pr03+f03;

end y 1 =delay1 (k); pro1 =o; for i=36.5:63

f0 1 =(prod(l :(n))./(prod(l 5). *prod( 1 :(n-i)))).*@sO."i).*(( 1 -psO)."(n-i)); prOl=prOl+fOl;

end pr13=0; y2=delay2(k);

for i=99.5: 126 fI3=Cprod(l:(2*n))./(prod(l: i).*prod(l:(2*n-i)))).*Cpsl ."i).*((l-ps 1)."(2*n-i)); pr13-pr13-tf13;

end prl l=O; for i=36.5:63

fl l=@rod(l :(n))./(prod(l :i).*prod(I :(n-i)))).*(psl ."i).*((l -p~l).~.(n-i)); prl l=prl l+f l l ;

end

plot(x,yl,'-',x,y2,'-*',x,y3,'--'); legend('type-I hybrid ARQt,'type-I1 hybrid ARQt,'type-I1 hybrid ARQkadaptive fair-queueing'); %plot(x,y2,'y');legend('type-I1 hybrid ARQ'); %plot(x,y3,'r');legend('type-I1 hybrid ARQ&adaptive fair-queueing'); xlabel('coding rates ----> '); ylabel('Average defay(ms)----> I);

k=55; n=55:79; %e0=0.0165; %e1=4.88*1 OA(-8); psO=O. 124; ps 1=0.00000039; pr03=0; for i=99.5: 126

f03=(prod(I :(2*n))./(prod(l :i).*prod(l:(2*n-i)))).*@~O.~i).*((l -p~0).~(2*n-i)); pr03=prO3-tf03;

end prOl=O; for i=36.5:63

f l l =Cprad(l :(n))./(prod(l :i).*prod(l :(n-i)))).*(psO."i).*I(l -psO)."(n-i)); prOl=prOl-tf01;

end prl3=0; for i=99.5: 126 fl3=(prod(l:(2*n))./(prod(l :i).*prod(l:(2*n-i)))).*@sl ."i).*((l -psl)."(2*n-i)); prl3=prl3+fl3;

end prl1=0; for i=36.5:63

fl l=(prod(l :(n))./(prod(l :i).*prod(l :(n-i)))).*(psl .Ai).*((l-psI).A(n-i)); prl l=prl l t f l l ;

end

t0=(1 -(pro1 .*pro 1 .*pro3 .*pr03))/(1+prO 1+(prO 1 .*pro1 .*pd3)- (pro 1 .*prOl. *pr03. "pr03)); tl=(l-(prl l.*prl l.*prl3.*pr13))/(1+prl l+@rl l.*prl l.*prl3)- tprl l.*prl Zl*p-l3.*prl3)); n=55:79; yl=to(); y2=to; y3=t2(); x=[ 0.72 0.725 0.735 0.75 0.775 0.8 0.825 0.85 0.875 0.9 0.925 0.95 0.975 I];

plot (x,yl ,'-',x,y2,'-*',x,y3,'--');legend ('type - I hybrid ARQ','type - I1 hybrid ARQ1,'type - I1 hybrid ARQ&adaptive fair-queueing'); %plot (x7y2,Y ');legend ('type - I1 hybrid ARQ'); %plot (x,y3,'Pf);legend ('type - I1 hybrid ARQ&adaptive fair-queueing'); %plot(x,yl ,'k-',~,y2,'k"-',~,y3,'k*-',x,y4,'k.-',x,y5,'k--'); axis(l0.72 1 0.7 11); %legerid('type-I hybrid ARQ', 'type-I1 hybrid ARQ', 'type-11 hybrid ARQ&adaptive fair- queueingl,'type-I hybrid ARQ(analysis)','type-I1 hybrid ARQ(ana1ysis)'); xlabel('coding rates R=Wn k=55'); ylabel('throughput');

Simulation Programs of Decentralised CAC

%eff.bw and equvi.capacity knction B=cac(B 1); clc; clear all; Psu l=[]; bw 1 =[I; eb 1 =I]; c 1 =[I; %Xcc=5; N=5; t 1 =[I; %ad= 10; pbr=2O*(l OA(-6));xa l=[]; Asc=1 .30A(-3); Xbc= 150; %x1=150; %xl=l; Psu=(1/40); %p 1 =0.4; %p 1 =2; clr= 1 OA(-2); Bbs=150; Np= 1 0; d=-Iog(clr)lBbs; %x=[1.40 0.3 1.20 0.1 1.09 0.08 1.07 0.06 1.05 0.041; %x=[500 56 57 5001; x=[2120 1060530265 I28 6432 16 841; t=O; j=1; for n= 1 :Np,

y= 1 in; z=o; for i= 1 :n,

%x=rand( 1 ); %disp(x);

z=z+exp(d*x(i)); end %for t=0:20:200,

xaG)=t; aG)=(l/t)*log(y*z); disp(ati1); bw(j)=(aQ)/d); %t=t+20; xa 1 =[xal ,xa];

%end %plot(xa,eb);

%for Psu=0:20:200, s=Asc*t*( 1 -Psu)-Xbc; u=sqrt((((Asc*t)*(l -P~u))-Xbc)~2); g=(4*Xbc*P~~*Asc*t"(l -Psu)); n 1 =4*Asc*t*( 1 -Psu); t=t+20; c(j)=(l -pbr)*((s+u+g)/~~l); eb=bw-clj); j=j+ 1 ; Psul =[Psu 1 ,Psu]; bw 1 =[bw 1 ,bw]; c 1 =[c 1 ,c]; tl=[tl ,t]; eb 1 =[eb 1 ,eb]; disp(b w) ;

end for k=1:10, if eb(k)<bw(k)

disp('Accept the Connection'); else

disp('Reject the connection');

end k=k+ 1 ; end subplot(2,2,1); plot(xa,eb,'k-*',xa,bw,'k: *I); xlabel('tirne,slots'); ylabel('Bandwidthl); legend('estimatedf,'available'); title('Estimation of Bandwidth'); %T=[T,tJ; %C=[C,c]; %BW=[B W,bw]; %plot(BW);

% TO compare the throughput of Decentralised and centralised % CENTRALJSED b c t i o n T=cacthral3(T 1);

PL 1 =4; PL2=0; PL2=[]; i= 1 ; j=O; %DP=23.2+4*((34+x)/(Bps/(l OA6)), DP=O; %CD=PR+PLI +DP; for j= 1 :5, DPCj)=23.2+4*((34+x(i))/(Bps(j)/(( 1 OA4)/60))); CD=PR+PLI +DP('j);

end Tp=O; i=l; for PL= 10: 100: 1000,

Tp(i)=(PL*2)/(CD); %Tp(i)=PL/(CD); ~=i+l ; PL2=[PL2,PL];

end disp(Tp); %semilogy(PL2,Tp,'k-*I);

% DECENTRALISED Lbch=9; Lfch=6; Lach=3; Lrch=7; Bps=3 0; Lul=4+(9/Bps}; Llch=5OO-(Lbch+Lfch+Lach+Lul+Lrch); Npdu=(Llch*Bps/54); X=[1234005006007008009001000]; t=O; for i=1:0.01:10, t(i)=Npdu*(X(i)*O.00048/1 OO)/(((X(i))+4)*0.002); disp(t);

end if t>Tp

disp(Decentra1ised has highest thr~ughput'); else

disp('Centra1ised has highest throughput'); end subplot(2,2,4);

plot(X,t,'k: *',PL2,Tp,'k-*'); xlabel(No.of Time slots(s)'); yiabel('Throughput'); legend('Decentralisedt,'Centralised'); title('Decentra1ised Vs Centralised');

clc; clear all; exno=[l 2 3 4 5 ] hoeqno=[Q. I 0.2 0.3 0.4 0.51; reqcall=input('Enter the call value= '); newcall=input('Enter the newcall value= I);

Tn=5; %for class = 1 :4,

%exn0(~la~~)=e~n0(~1as~)+ 1 ; %end

if(reqcall==newcall) for i=l :Tn, eqno(i)=exno(i)+hoeqno(i);

end end If--.input('Enter the value of last flag= I); qq=input('Enter the value QoS guarantee= '); if qq==lf

cIass=input('Enter the class vaIue= '); CBR=input('Enter the value of CBR= '); if class=CBR

jitter=cbrc2(1); jb=input('Enter the value of jitter bounds= '); if jitter>jb

99-0; disp(Cannot admit the call');

else disp('Admit the new call as CBR');

end else

cc=input('Current calculated value= '); cc=cc+ 1 ; Ivbr=input('Enter the value of lvbr= '); if cc==lvbr

lf=O; db=input('Enter the delay bound= 3; delay=vbw2( 1);

if delay>db qq=O; cc=cc+ 1 ; If=O; disp('Admit the new call as VBR');

end else

dispflCannot admit the new call'); if cc==lvbr

lf=O; end

end end

end if qq-1

disp(Wew call is blocked'); end

% To compare the throughput of Decentralised and centralised clc; close all;% CENTRALISED PR=20; %x=3; x=[30 40.5 60 90 180 260 340 450 540 6001; Bps=[6 9 12 18 36 45 67 78 89 1001; PL 1 =4; PL2=0; PL2=[]; i=l; j=O; %DP=23.2-t4*((34+x)l(Bps/(l OA6))); DP=O; %CD=PR+PLl +DP; forj=l:lO, DP(j)=23.2+4*((34+x(j))/(Bps(j)/((l OA4)/60))); CD(j)=PR+PLl -i-DPg');

end Tp=O; i=1; for PL=10:200: 1000,

Tp(i)=(PL*2)/(CD(i)); %Tp(i)=P W (CD); i=i+l ; PL2=[PL2,PL];

end

% DECENTRALISED Lbch=9; Lfch=6; Lach=3; Lrch=7; Bps=30; Lul=4+(9/Bps); Llch=5OO-(Lbch+Lfch+Lach+Lult-Lrch); Npdu=(Llch*Bps/53); X=[1 2 3 400 500 600 700 800 900 IOOO]; t=o; for i=1:0.01:10, t(i)=Npdu*(X(i)*O.00048/1 OO)/(((X(i))+4)"0.002); t 1 (i)=Npdu*(X(i)*O.O004 8/ 1 OO)/(((X(i))+4)*0.02) disp(t);

end pIot(X,t,'k:*',PL2,Tp,'k-"'); xlabel(Wo.of Time slots'); ylabel('Throughput'); legend('Decentralised', 'Centralised');

%eff.bw and equvi.capacity clc; clear all; Psu 1 =[I; bwl=[]; eb 1 =[I; cl=[]; %Xcc=5; N=5; tl=[]; %ad= 10; pbr-20*(l W(-6));xa l=[1; Asc=1.30"(-3); Xbc= 1 50; %x1=150; %xl=l; Psu=( 1 /40); %p 1-0.4; %p l=2;

clr= l OA(-2); Bbs=150; Np= 1 0; d=-log(clr)/B bs; %x=[1.40 0.3 1.20 0.1 1.09 0.08 1.07 0.06 1.05 0.041; %x=[500 56 57 5001; x=[21201060530265128 643216841; t=O; j=1; for n= 1 :Np, y- l/n; 250; for i= 1 :n,

%x=rand( 1 ); %disp(x);

z=z+exp(d*x(i)); end %for t=0:20:200,

xa(i)=t; a(j)=(l /t)*Iog(y*z); disp(a0')); bw(j)=(a(j)/d); %t=t+20; xal=[xal ,xa]; %end

%pIot(xa,eb); %for Psu=0:20:200, s=Asc*~ *( 1 -Psu)-Xbc; u=sqrt((((Asc*t)*(l -Psu))-Xbc)"2); g=(4*Xbc*Psu*Asc*t*( 1 -Psu)); nl=4*Asc*t*(l-Psu); t=t+20; cG)=(l -pbr)*((s+u+g)/n 1); eb=bw-c(j); j=j+l; Psul=[Psul,Psu]; bwl=[bwl ,bw]; c 1 =[c 1 ,c]; tl=[tl,t]; ebl=[ebl ,eb]; disp(bw);

end for k=1:10, if eb(k)<bw(k)

disp('Accept the Connection'); else

disp('Reject the connection');

end k k + 1 ; end plot(xa,eb,'k-*',xa,bw,'k:*'); xlabel('time(s1ots)'); ylabel('Bandwidth(spaces)'); legend('estimatedt,'avaiIable');

% max no. of connections %pr== 1 00; clc; close all; a= 1 0; %pr=200; N=10; ps=0.9; 1=0.4; r=0.2; i=l; %T= 10; pr=0.9; for T=0:20:200,

xax(i)=T; z=((aA2) * (2-pr));

x=l 6*r*(psA2);6 y=8*pr*((l*T)+(r*ps)-N); %y 1 =&*pr*(l *T+r*ps-N); %y(i)=8*pr*(I*T+r*ps-N); % y(i)=r; k(i)=( 1 /(2*pr))*(z+(4*N)+(4*1 *T)-2 *r*ps-a*(sqrt(((aA2)* (2-pr)A2)+(16*N)+y+x))); %xax(i)--pr; i=i+ 1 ; end j=1; for prl=O:20:200,

prx(j)=pr 1 ; lCj)=(prl *ps+a)/ 1 0; j=j+ 1 ; end

%disp(k); %disp(z); %plot(xax,k); plot(xax,k,'k-*',prx,l,'k:*"); xIabel('time(slots)'); ylabel(TJo.of Connections'); legend('Decentralised','Centralised');

clc; close ail; C=(1-0.05)*(1-0.03)*(1-0.03); C 1=(1-0.05)*(1-0.03);

TCI=C1/2; disp(TC 1); %Th=I 00*(1 W(-3)); %Th2=[]; i= 1; j= 1 ;D=0; C=O; I= 1 00; Th2=[]; for Thl=l:lO:lOO, AV(i)=Th 1 /(2*( 1 -TC)); AVI (i)=Thl/(2*(1 -TCl)); CCj)=(AV(i)*TC); D('j)=(AVl (i)*TC l)/l 0; i=i+l; j=j+ 1 ; ThZ=[Th2,Thl]; end %end disp(C); plot(Th2,C,'k-*',ThZ,D,'k:*'); xlabel('Ho1ding Time'); ylabel('Max Delay(ms)'); legend('Cmtra1ised ','Decentralised');

% Algorithm for Decentralised Call Admission Control clc ; clear all; conn=input('Enter the value of connection= 3; f=input('Enter the value fixed Connection= '); if conn==f

%estimate bandwidth Ebandwidth=cac( 1 ); %determine no.of connections Connection=cacconnal2( 1); delay=cacdelayaf3(1); throughput=cacthral3(1);

else BS=input('Enter the value of Bandwidth= '); Allocate=input('Enter the allocation= '); if(BS==AIlocate) Cor~ecticn=cacconna12(1); disp('Accept the connection'); delay=cacdelayal3(1); throughput=cacthral3(1);

else disp('Re1ease the Connection');

end end %calculate Delay