Universitas Sumatera Utara

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2 Lampiran 1 function [PN1]=pnsequence(d) G=d*2; % Code length %Generation of first m-sequence using generator polynomial [45] sd1 =[ ]; % Initial state of Shift register PN1=[]; % First m-sequence for j=1:g PN1=[PN1 sd1(5)]; if sd1(1)==sd1(4) temp1=0; else temp1=1; sd1(1)=sd1(2); sd1(2)=sd1(3); sd1(3)=sd1(4); sd1(4)=sd1(5); sd1(5)=temp1; Lampiran 2 %Simulasi AWGN channel tanpa channel coding clear;clc; %input panjang data d=100; r=1; n=45; %Definisi rentang nilai EbNo ebno=1:1:20; %Generate data integer dengan distribusi uniform data=randint(1,d,4); %Pengubahan ke data biner data_bit1=de2bi(data,'left-msb'); %Pengaturan data biner menjadi 1 kolom for i=1:1:length(data_bit1); data_bit11((2*i)-1:2*i,1)=[data_bit1(i,1) data_bit1(i,2)]; data_bit11=data_bit11'; %Generate fungsi PN Sequence [PN1]=pnsequence(d); %Data di-xor-kan dengan PN Sequence if n==45 data2=xor(data_bit11,pn1); PN=PN1;

3 %Pengaturan kembali data menjadi 2 kolom for i=1:length(data_bit1) data_bit12(i,1:2)=[data2(1,(2*i-1)) data2(1,2*i)]; %Perubahan kembali bit ke integer data3=bi2de(data_bit12,'left-msb'); %Modulasi QPSK data_mod=pskmod(data3,4); %Penambahan kanal AWGN for e=1:length(ebno) data_aw(:,e)=awgn(data_mod,ebno(e)); %Proses demodulasi for x=1:length(ebno) data_demod(:,x)=pskdemod(data_aw(:,x),4); %Data hasil demodulasi di konversi terlebih dahulu ke biner %Kemudian di-xor-kan kembali dengan PN Sequence for x=1:length(ebno) data_bit2=[]; data_bit2=de2bi(data_demod(:,x),'left-msb'); [data_bit22]=konversi(data_bit2,pn); data4(:,x)=bi2de(data_bit22,'left-msb'); for y=1:length(ebno) BER(1,y)=sum(data~=data4(:,y)')/d; plot(ebno,ber,'b'); title('grafik EbNo terhadap BER pada kanal AWGN dengan pengkodean kanal'); xlabel('ebno (db)'); ylabel('ber'); Lampiran 3 %Convolutional Encoder ; input=1 bit -> output=2 bits with 3 memory elements, Code Rate=1/2 function [encoded_sequence]=convlenc(message) %TEST MESSAGES % message=[ ];%prb 0-1 % message=[ ];

4 % message=[ ];%prb 0-1 % message=[ ]; % message=[ ];%prb 0-1 % message=[ ]; % message=[ ];%prb 0-1 % message=[ ]; % message=[ ];%prb 0-1 % message=[ ];%prb 0-1 % message=[ ]; % message=[ ];%prb 0-1 % message=[ ];%prb 0-1 % message=[ ]; % message=[ ];%prb 0-1 enco_mem=[0 0 0]; %# of memory elements=3 encoded_sequence=zeros(1,(length(message))*2); enco_mem(1,3)=enco_mem(1,2); enco_mem(1,2)=enco_mem(1,1); enco_mem(1,1)=message(1,1); temp=xor(enco_mem(1),enco_mem(2)); o1=xor(temp,enco_mem(3)); polynomial=111 o2=xor(enco_mem(1),enco_mem(3)); polynomial=101 encoded_sequence(1,1)=o1; encoded_sequence(1,2)=o2; %generator %generator msg_len=length(message); c=3; for i=2:msg_len enco_mem(1,3)=enco_mem(1,2); enco_mem(1,2)=enco_mem(1,1); if(i<=msg_len) enco_mem(1,1)=message(1,i); else enco_mem(1,1)=0; temp=xor(enco_mem(1),enco_mem(2)); o1=xor(temp,enco_mem(3)); o2=xor(enco_mem(1),enco_mem(3)); encoded_sequence(1,c)=o1; polynomial(1,1,1) c=c+1; encoded_sequence(1,c)=o2; polynomial(1,0,1) c=c+1; %o1 generating %o2 generating

5 Lampiran 4 %Hard Decision Viterbi Decoder %Function gets an encoded message 'rcvd(encoded by a convolutional encoder) %as argument and returns the decoded message 'dec_op' function [dec_op]=viterbidec(rcvd) %Concatenate two consecutive bits of recieved encoded sequence to %make up a symbol input=[]; for j=1:2:length(rcvd) input=[ input (rcvd(j))* 2 + (rcvd(j+1))]; %initializing all arrays op_table=[ ; ; ; ]; %OUTPUT array ns_table=[0 0 2; 1 0 2; 2 1 3; 3 1 3]; %NEXT STATE array transition_table=[ ; ; ; ]; % A R R A Y S - U P D A T I N G Part st_hist(1:4, 1:17)=55; %STATE HISTORY array aem=zeros(4, 17); %ACCUMULATED ERROR METRIC (AEM) array ssq=zeros(1, 17); %STATE SEQUENCE array % input=rcvd; %input(1, :)=bin2dec(rcvd) %input=[ ] %INPUT vector %rcvd=['00';'11';'11';'00';'01';'10';'01';'11';'11';'10';'00';'00' ;'11';'00';'11';'10'; '11'] lim=length(input); %number of clock cycles for (t=0:1:lim) %clock loop % disp(' ') t; %display current clock instance if(t==0) st_hist(1,1)=0; %start at state 00 else temp_state=[];%vector to store possible states at an instant temp_metric=[];%vector to store metrics of possible states temp_parent=[];%vector to store parent states of possible states

6 for (i=1:1:4) i; in=input(t); if(st_hist(i, t)==55) %if invalid state %do nothing else ns_a=ns_table(i, 2)+1; %next possible state-1 ns_b=ns_table(i, 3)+1; %next possible state-2 op_a=op_table(i, 2); op_b=op_table(i, 3); cs=i-1; %next possible output-1 %next possible output-2 %current state M_a=hamm_dist(in, op_a); %branch metric for ns_a M_b=hamm_dist(in, op_b); %branch metric for ns_b indicator=0; %flag to indicate redundant states for k=1:1:length(temp_state) %check redundant next states %if next possible state-1 redundant if(temp_state(1,k)==ns_a) indicator=1; %ADD-COMPARE-SELECT Operation %em_c: error metric of current state %em_r: error metric of redundant state em_c=m_a + aem(i,t); em_r=temp_metric(1,k) + aem(temp_parent(1, k)+1,t); if( em_c< em_r)%compare the two error metrics st_hist(ns_a,t+1)=cs;%select state with low AEM temp_metric(1,k)=m_a; temp_parent(1,k)=cs; %if next possible state-2 redundant if(temp_state(1,k)==ns_b) indicator=1; em_c=m_b + aem(i,t); em_r=temp_metric(1,k) + aem(temp_parent(1, k)+1,t); if( em_c < em_r)%compare the two error metrics st_hist(ns_b,t+1)=cs;%select state with low AEM temp_metric(1,k)=m_b; temp_parent(1,k)=cs; %if none of the 2 possible states are redundant if(indicator~=1)

7 %update state history table st_hist(ns_a,t+1)=cs; st_hist(ns_b,t+1)=cs; %update the temp vectors accordingly temp_parent=[temp_parent cs cs]; temp_state=[temp_state ns_a ns_b]; temp_metric=[temp_metric M_a, M_b]; %print the temp vectors temp_parent; temp_state; temp_metric; %update the AEMs (accumulative error metrics) for all states for current instant 't' for h=1:1:length(temp_state) xx1=temp_state(1, h); xx2=temp_parent(1, h)+1; aem(xx1, t+1)=temp_metric(1, h) + aem(xx2, t); % of clock loop % T R A C E - B A C K Part for(t=0:1:lim) slm=min(aem(:, t+1)); slm_loc=find( aem(:, t+1)==slm ); sseq(t+1)=slm_loc(1)-1; dec_op=[]; for p=1:1:length(sseq)-1 p; dec_op=[dec_op, transition_table((sseq(p)+1), (sseq(p+1)+1))]; Lampiran 5 %Simulasi AWGN channel dengan convolutional coding clear;clc; %input panjang data d=100; r=1; n=45; %Definisi rentang nilai EbNo ebno=1:1:20; %Generate data integer dengan distribusi uniform

8 data=randint(1,d,4); %Pengubahan ke data biner data_bit1=de2bi(data,'left-msb'); %Pengaturan data biner menjadi 1 kolom for i=1:1:length(data_bit1); data_bit11((2*i)-1:2*i,1)=[data_bit1(i,1) data_bit1(i,2)]; data_bit11=data_bit11'; %Generate fungsi PN Sequence [PN1, PN2, PN3]=pnsequence(d); %Data di-xor-kan dengan PN Sequence if n==45 data2=xor(data_bit11,pn1); PN=PN1; %Proses Convolutional Encoder [encoded_sequence]=convlenc(data2); data_es=encoded_sequence; %Pengaturan kembali data menjadi 2 kolom for i=1:2*length(data_bit1) data_bit12(i,1:2)=[data_es(1,(2*i-1)) data_es(1,2*i)]; %Perubahan kembali bit ke integer data3=bi2de(data_bit12,'left-msb'); %Modulasi QPSK data_mod=pskmod(data3,4); %Penambahan kanal AWGN for e=1:length(ebno) data_aw(:,e)=awgn(data_mod,ebno(e)); %Proses demodulasi for x=1:length(ebno) data_demod(:,x)=pskdemod(data_aw(:,x),4); %Data hasil demodulasi di konversi terlebih dahulu ke biner %Kemudian di-xor-kan kembali dengan PN Sequence for x=1:length(ebno) data_bit2=de2bi(data_demod(:,x),'left-msb'); for i=1:1:length(data_bit2); data_bit21((2*i)-1:2*i,1)=[data_bit2(i,1) data_bit2(i,2)]; data_bit21=data_bit21'; [dec_op]=viterbidec(data_bit21);

9 data_decod=dec_op; data_var=xor(data_decod,pn); for i=1:d data_bit22(i,1:2)=[data_var(1,(2*i-1)) data_var(1,2*i)]; %[data_bit22]=konversi(data_bit2,pn,2); data4(:,x)=bi2de(data_bit22,'left-msb'); for y=1:length(ebno) BER(1,y)=sum(data~=data4(:,y)')/d; plot(ebno,ber,'r'); title('grafik EbNo terhadap BER pada kanal AWGN tanpa pengkodean kanal'); xlabel('ebno (db)'); ylabel('ber'); Syntax Matlab untuk Gambar 4.6 %awgn tanpa channel coding x=[ ]; y=[ ]; n=5; p=polyfit(x,y,n); xawgnnocoding=linspace(1, 20, 1); yawgnnocoding=polyval(p, xawgnnocoding); semilogy(x, y, 'b*-.', xawgnnocoding, yawgnnocoding) hold on axis manual; axis([ ]); xlabel('eb/no'); ylabel('ber'); title('ber of AWGN without channel coding') Syntax Matlab untuk Gambar 4.7 %awgn dengan channel coding rate=1/2 x=[ ]; y=[ ]; n=5; p=polyfit(x,y,n); xawgncoding=linspace(1, 20, 1); yawgncoding=polyval(p, xawgncoding); semilogy(x, y, 'ro-.', xawgncoding, yawgncoding) axis manual; axis([ ]);

10 xlabel('ebno'); ylabel('ber'); title('ber of AWGN with channel coding') Syntax Matlab untuk Gambar 4.8 %awgn tanpa channel coding x=[ ]; y=[ ]; n=5; p=polyfit(x,y,n); xawgnnocoding=linspace(0, 20, 1); yawgnnocoding=polyval(p, xawgnnocoding); semilogy(x, y,'b*-.'); hold on %awgn dengan channel coding rate=1/2 x=[ ]; y=[ ]; n=5; p=polyfit(x,y,n); xawgncoding=linspace(0, 20, 1); yawgncoding=polyval(p, xawgncoding); semilogy(x, y,'ro-.'); axis manual; axis([ ]);

The Viterbi Algorithm EECS 869: Error Control Coding Fall 2009

1 Bacground Material 1.1 Organization of the Trellis The Viterbi Algorithm EECS 869: Error Control Coding Fall 2009 The Viterbi algorithm (VA) processes the (noisy) output sequence from a state machine