COM-302 — Robust Communication Over a Noisy Channel

EPFL Principles of Digital Communications final project: transmit a 40-character text message through an adversarial server channel and recover it without a single bit error, under a strict energy budget of 1500.

The scheme is M-ary orthogonal signaling using a Hadamard (Walsh) code — each of the M=4096 messages is mapped to one row of a 2¹⁵×2¹⁵ Hadamard matrix, and all codewords are mutually orthogonal.

The channel

For every block of two symbols (X₁, X₂), the server secretly picks one of two branches and attenuates the other by √G with G = 10, then adds Gaussian noise to both. The receiver never learns which branch was kept — it has to figure it out from the received signal alone.

Approach

The transmitter maps every 2 characters (12 bits, 4096 possibilities) to a single Hadamard codeword of length N = 2¹⁵ = 32768, built as a one-hot vector pushed through a Walsh–Hadamard transform. This turns the problem into orthogonal signaling on a massive codebook, so the receiver only has to find the loudest correlation.

The receiver runs a batched Fast Walsh–Hadamard Transform on the two sub-channels in parallel, combines them with the two possible branch hypotheses, and picks the codeword with the highest score. No matrix is ever materialized — decoding 20 codewords of length 32k is essentially free.

Highlights:

• Fast Walsh–Hadamard transform, fully vectorized and batched — encodes/decodes in O(N log N) with zero explicit matrices, so memory stays flat as r grows.
• Joint two-branch ML decoder that marginalizes over the channel's hidden branch selection in a single pass.
• Energy-optimal scaling: codeword amplitude is computed analytically from the budget so the signal rides right at the limit of what the server allows.
• Bit-perfect recovery of the 40-character message through the real EPFL server (iscsrv72.epfl.ch).

Layout

PDC_project/
  main.py          # end-to-end pipeline: encode → send → receive → decode
  transmitter.py   # Hadamard encoder with k-character packing
  receiver.py      # batched FWHT ML decoder
  utils.py         # fast + batched Walsh–Hadamard transforms, alphabet, G
  client.py        # official EPFL channel client
  fake_client.py   # local channel simulator for offline testing
  test_accuracy.py # BER sweeps across parameters
PDF/               # project description and theory notes

Run it

cd PDC_project
echo "your 40-character message goes here........" > message_in.txt
python3 main.py

The pipeline encodes the message, uploads the waveform to the EPFL server, downloads the noisy response, decodes it, and prints whether the recovered text matches the original.