Error Correction Capability of Viterbi Decoder

Hello folks,

I am using fec encoding followed by viterbi decoding. In this process, I observed that the viterbi decoder error correction capability doesn't go hand in hand with theoretical calculations.

For example, in this case, I am using 1/2 rate convolutional encoder for encoding. Theoretically, for 1/2 rate, dfree = 10 and according to error correction capability t = (df-1)/2 , which will intend to 4.5 approximating it to 4. This means, that it should correct 4 errors atleast.

In the following code, I am introducing two errors (randomly) for every 14 bits, vitdec is unable to correct them, it works fine when I introduce one error.

Can someone help me in understanding the reasoning behind it ? Your help will be highly appreciated. Thank you!

clc;clearvars;
%%Random Binary Generator
dataIn = randi([0 1],700,1);

%%Convolutional Encoder 1/2 rate
t = poly2trellis(7,[171,133]);
coderate = 1/2;
encoded = convenc(dataIn,t);

%%flip one bit for every 7 bits to introduce errors
for i = 1:14:(length(encoded))
    temp = encoded(i:i+13);
    u = randi([1 13],1,2);    
    temp(u(1)) = ~temp(u(1)); % one error
    temp(u(2)) = ~temp(u(2)); % comment out to check for one error
    encoded(i:i+13)= temp;
end

%%viterbi decoder
tbl = 30;
dataOut = vitdec(encoded,t,tbl,'cont','hard');
numErrsInFrameHard = biterr(dataIn(1:end-tbl),dataOut(tbl+1:end));
display(numErrsInFrameHard)

Answer 1

[Fatin Farihah Mohd]

I got the same problem.. The maximum error can be corrected by Viterbi decoder is 2 bits only. Iam not sure about the formula.