Viterbi decoder MATLAB source code

This section of MATLAB source code covers viterbi decoder matlab code including viterbi decoder specifications for convolutional encoder of constraint length 5.

Specifications of convolutional encoder

Convolution Encoder (3, 1, 4) specifications
Coding rate: 1/3
Constraint length: 5
Output bit length: 3
Message bit length: 1
Maximal memory order / no. of memory elements = 4
Generator Polynomials: 25 (8), 33 (8), 37 (8)

Specifications of viterbi decoder

codeword length: 20
coding rate: 1/3
constraint length: 5
trace back length: 20
quantization levels: two (Hard decision type)
generator Polynomials: 25 (8), 33 (8), 37 (8)

This viterbi is designed for the above convolutional encoder specifications. Refer convolution encoder basics and Convolutional Encoder matlab code.


Viterbi MATLAB Code

function [dec_op]=viterbi_decoder(rcvd)
%Concatenate three consecutive bits of received encoded sequence to
%Make up a symbol
input=[];
for j=1:3:length(rcvd)
input=[ input (rcvd(j)* 2^2) + (rcvd(j+1) * 2^1) + (rcvd(j+2) * 2^0)];
end

%%Initialize Ouput Table
Output_Table = [ ...
0 0 7; ...
1 7 0; ...
2 3 4; ...
3 4 3; ...
4 5 2; ...
5 2 5; ...
6 6 1; ...
7 1 6; ...
7 3 4; ...
8 4 3; ...
9 0 7; ...
10 7 0; ...
11 6 1; ...
12 1 6; ...
13 5 2; ...
14 2 5];

%%Initialize Next-State(Ouput State) Table
Next_State =[ ...
0 0 8; ...
1 0 8; ...
2 1 9; ...
3 1 9; ...
4 2 10; ...
5 2 10; ...
6 3 11; ...
7 3 11; ...
8 4 12; ...
9 4 12; ...
10 5 13; ...
11 5 13; ...
12 6 14; ...
13 6 14; ...
14 7 15; ...
15 7 15];

%%%Updating the arrays
State_Hist(1:16, 1:10)=55; %STATE HISTORY array
aem(1:16, 1:6)=0; %ACCUMULATED ERROR METRIC (AEM) array
%%%%%%%%%Transition Table For Trace Back%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Transition_Table = [ ...
0 55 55 55 55 55 55 55 1 55 55 55 55 55 55 55; ...
0 55 55 55 55 55 55 55 1 55 55 55 55 55 55 55;...
55 0 55 55 55 55 55 55 55 1 55 55 55 55 55 55;...
55 0 55 55 55 55 55 55 55 1 55 55 55 55 55 55;...
55 55 0 55 55 55 55 55 55 55 1 55 55 55 55 55;...
55 55 0 55 55 55 55 55 55 55 1 55 55 55 55 55;...
55 55 55 0 55 55 55 55 55 55 55 1 55 55 55 55;...
55 55 55 0 55 55 55 55 55 55 55 1 55 55 55 55;...
55 55 55 55 0 55 55 55 55 55 55 55 1 55 55 55;...
55 55 55 55 0 55 55 55 55 55 55 55 1 55 55 55;...
55 55 55 55 55 0 55 55 55 55 55 55 55 1 55 55;...
55 55 55 55 55 0 55 55 55 55 55 55 55 1 55 55;...
55 55 55 55 55 55 0 55 55 55 55 55 55 55 1 55;...
55 55 55 55 55 55 0 55 55 55 55 55 55 55 1 55;...
55 55 55 55 55 55 55 0 55 55 55 55 55 55 55 1;...
55 55 55 55 55 55 55 0 55 55 55 55 55 55 55 1];

%%%find the length of input
lim=length(input); %number of time cycles
State_Hist(1,1)=0; %%Initialze the starting state at t1 = 0;

%%%%%%%%%LOOP FOR NUMBER OF TIME UNITS%%%%%%%%%%%%%%%%
%%Loop L1 Start
for t=1:1:lim
t;
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
%%%%%%%%%%%%%LOOP FOR NUMBER OF STATES
%%%Loop L2 Start
for i=1:16
in=input(t);
%%check if the present state is valid or not
if( State_Hist(i,t)==55) %if the statement is true than its an invalid state
%%Do Nothing

else
NS_a = Next_State(i,2) + 1; %%Next possible state 1
NS_b = Next_State(i,3) + 1; %%Next possible state 2
OP_a = Output_Table(i,2); %%Possible output 1
OP_b = Output_Table(i,3); %%Possible output 1
CS = i - 1; %%Current State
M_a = hamm_dist(OP_a,in); %%Branch Metric for NS_a
M_b = hamm_dist(OP_b,in); %%Branch Metric for NS_a
Flag = 0; %Flag to indicate redundant states
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%CHECKING FOR 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)
Flag=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
State_Hist(NS_a,t+1)=CS;%select state with low AEM
temp_metric(1,k)=M_a;
temp_parent(1,k)=CS;
end
end
%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
State_Hist(NS_b,t+1)=CS;%select state with low AEM
temp_metric(1,k)=M_b;
temp_parent(1,k)=CS;
end
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%% END %%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%if none of the 2 possible states are redundant
if(Flag == 0)
%update state history table
State_Hist(NS_a,t+1) = CS;
State_Hist(NS_b,t+1) = CS;
%update the temp vectors accordingly
temp_state = [temp_state NS_a NS_b];
temp_parent = [temp_parent CS CS];
temp_metric = [temp_metric M_a M_b];
end
end
end %%loop L2 i.e State loop ends here
%Update the AEMs (accumulative error metrics) for all states for
%current instant 't'

for h=1:1:length(temp_state)

x1 = temp_state(1,h); %finding the temp_state
x2 = temp_parent(1,h) + 1; %finnding the parent_state of the present temp state
aem(x1,t+1) = temp_metric(1,h) + aem(x2,t);
end
end
%%loop for l1 i.e time ends here

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% T R A C E - B A C K
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
slm = min(aem(:, 21));
slm_loc =find( aem(:, 21)==slm );
sseq(21) = (slm_loc(1)-1);

for t=20:-1:1
sseq(t) = State_Hist(sseq(t+1) + 1,t+1);
end

dec_op=[];
for k =1 : 20
dec_op(k) = Transition_Table(sseq(k)+1, sseq(k+1)+1);
end

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