# Probability of Error vs Noise

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sid101 on 3 May 2020
Answered: Sai Sri Pathuri on 6 May 2020
I want to create a binary bit stream and introduce gaussian errors and then relate the level of noise to Bit error rate using erfc(sqrt(Eb/N0) as the target metric.
To create a bit stream and introuducing Gaussian errors, I am using:
bit_stream = randi([0 1],1000,1);
noisy_stream = awgn(bit_stream, 20);
How can I calculate Eb/N0 from the noisy bit stream?
Image Analyst on 3 May 2020
If the signal is binary (zeros and ones), then how can you add Gaussian amplitude noise? Well, if you do, it will be analog. Unless the noise is extraordinarily high, it will have no effect once the noise is digitized again - this is the main benefit of digitization in the first place. Occasionally though there is such super high noise that can flip a bit and that's why they double check with things like CRC codes.

Sai Sri Pathuri on 6 May 2020
You may use SNR to find the Eb/No ratio.
1. Calculation of SNR:
You may use snr function to find the signal to noise ratio of noisy_stream signal
snrdB = snr(bit_stream, noisy_stream - bitstream);
2. You may use this documentation to find the relationship between SNR and Eb/No. You have to know the symbol period and sampling period of the signal (or) number of samples per symbol.
EbNo = snrdB + 10*log10(0.5*Tsym/Tsamp) - 10*log10(k); % For a complex signal
where, k might be influenced by the size of the modulation alphabet or the code rate of an error-control code