When noise stops being Gaussian: LDPC codes under heavy tails
What happens to an LDPC-coded 64-QAM link when the noise has heavy tails instead of following the textbook AWGN model.
Most textbook analysis of digital links assumes additive white Gaussian noise (AWGN). It is a convenient model, but real channels are not always that polite. Impulsive interference produces noise with heavy tails: most samples are small, and a few are very large.
In a project with Politecnico di Milano and Nokia, I studied what this does to a modern coded link.
The setup
- Modulation: 64-QAM
- Coding: LDPC
- Noise models: AWGN and Student’s t-distributed noise
- Metric: bit error rate (BER) as a function of SNR, from MATLAB simulations
What we saw
Under Gaussian noise, the LDPC-coded link behaved as expected and stayed robust. Under t-distributed noise, reaching the same error performance required a higher SNR.
One intuition: with heavy tails, occasional large noise samples push symbols far across the decision boundaries of a dense constellation like 64-QAM. On top of that, the soft information given to the decoder is usually computed under a Gaussian assumption, so it no longer matches the real channel.
Takeaway
The noise model is part of the receiver design, not a detail of the simulation. If the channel is not Gaussian, a receiver built only for Gaussian noise leaves performance on the table.