computation bit error as sum(abs)

Question

I am working on a realisation the convolutional encoder/decoder with constraint length K=7. Encoder and decoder were implemented and currently I am testing these functions

My test file looks like:

snr = 0.2;
len = 1000;
Din = GenData(len);  % generate a random data
% Encoder
EncOut = VitEnc(Din, len);

% create a channel 
noise = 10^(-snr/20);
    for i = 1: len,
        for j = 1: 2
            ChannelOut(j,i) = (EncOut(j,i) + (noise * randn));
            
            ChannelOut(j,i) = ChannelOut(j,i) * 2;
            if  ChannelOut(j,i) > 7     ChannelOut(j,i) = +7; end;
            if  ChannelOut(j,i) < -8    ChannelOut(j,i) = -8; end;
        end;
    end;
% Decoder 
DecOut = vitdec(len, ChannelOut);  

The last my step is computation bit error. It was suggest to use the following equation:

BitError = sum(abs( Din - DecOut));

If i add this equation in my simulation, I will get a number. For example, ´BitError = 27´. Could someone explain what the result of ´BitError ´ means? Is a bigger or a smaller number better?

EDIT 1:

1. I have thougth to compute bit error as a difference between input data and decoded data, but it was suggested to take a sum of the differences...I dont understand why?

Answer 1

BitError = sum(abs( Din - DecOut));

Assuming Din is the input data sequence and DecOut is the decoded output sequence.

Din - DecOut will compute the differences of the sequences. For example:

Din = [0 1 1 1 0]
DecOut = [0 1 0 1 1]
Din - DecOut = [0 0 1 0 -1]

Taking the absolute value returns a 1 in all of the location where there was a bit error and a zero where the bits are the same:

abs([0 0 1 0 -1]) = [0 0 1 0 1]

Now summing over that result tells you the total number of bit errors.

In general, more bit errors are worse and fewer bit errors are better as the goal is usually to faithfully reproduce the signal.