Hi Ahmed,
I understand that you are looking for a general formula and MATLAB code to implement convolutional coding with soft-decision decoding for any modulation type.
In order to implement convolutional coding with soft-decision decoding in MATLAB, you can follow the steps below:
Define the Convolutional Encoder: Convolutional codes are defined by their constraint length and generator polynomials. For example, a common rate 1/2 encoder can be defined with a constraint length of 3 and generator polynomials [7, 5] in octal.
trellis = poly2trellis(3, [7 5]); % Constraint length 3, rate 1/2
Generate Random Data:Create a random binary data sequence to encode.
codedata = randi([0 1], 100, 1); % Example: 100 random bits
Encode the Data:Use the "convenc" function to encode the data using the defined trellis.matlabCopy codeencodedData = convenc(data, trellis);
Add Noise and Modulate:Modulate the encoded data and add noise to simulate a real-world channel. For soft-decision decoding, use a modulation scheme like BPSK.
codemodulatedData = 2 * encodedData - 1; % BPSK modulation
noisyData = awgn(modulatedData, 2); % Add Gaussian noise with SNR of 2 dB
Soft-Decision Decoding:Use the "vitdec" function for Viterbi decoding with soft-decision inputs.
decodedData = vitdec(noisyData, trellis, 5, 'trunc', 'unquant');
Refer to the documentation of "convenc" and "vitdec" functions to know more about their properties:
- https://www.mathworks.com/help/comm/ref/convenc.html
- https://www.mathworks.com/help/comm/ref/vitdec.html
Hope this helps!
