Viterbi Decoder MATLAB Source Code

This section provides MATLAB source code for a Viterbi decoder, including specifications for a convolutional encoder with a constraint length of 5. It outlines the code snippet and steps involved in developing the Viterbi decoder MATLAB code.

Specifications of Convolutional Encoder

• Convolutional Encoder: (3, 1, 4)
• 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 (octal), 33 (octal), 37 (octal)

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 (octal), 33 (octal), 37 (octal)

This Viterbi decoder is designed for the above convolutional encoder specifications. For more information on convolutional encoders, refer to the basics and the Convolutional Encoder MATLAB code.

Viterbi Decoder MATLAB Code STEPS

1. STEP-1: Concatenate three consecutive bits of the received encoded sequence to form a symbol.
2. STEP-2: Create a Transition Table for Trace Back.
3. STEP-3: Find the length of the input and loop for the number of time units.
4. STEP-4: Check for redundant states.

Viterbi Decoder MATLAB Code

The following is a snippet of the Viterbi decoder 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];

%%%%%%%%%%%%%%%%%%%
%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

External Resources

Register and download the following paper for more study:

• Design and Implementation of Convolution Encoder with Viterbi Decoder
• Shao07_phd.pdf