Principles of digital communication - Project

Authors:

• Mahdi Atallah
• Youssef Boughizane
• Yuri Chlebny
• Thomas Muller

Project description

Link to pdf file: Project description

System design

1. Split the message into blocks of k bits.
2. Encode each block with the method described in exercise 3.
3. Concatenate the encoded blocks to form the transmitted signal.
4. Send the signal through a channel.
5. Receive the signal and decode it block by block using the method described in exercise 3.

Choice of constants

• Choosing $k$: Let us first notice that the size of transmitted message is given by: len(message) $= n = 2^{k-1} \cdot \frac{240}{k}$. Therefore, knowing that $n \leq 500000$ and $k>0$ and we find: $$2^{k-1} \cdot \frac{240}{k} \leq 500000 \iff \frac{2^{k-1}}{k} \leq \frac{6250}{3}$$ By numerically testing values, we find that the biggest k that satisfies the above inequality is k = 16. Therefore, we must choose $0 < k \leq 16$. We choose $k = 12$ since it respects the bounds and empirically doesn't take too much time to compute.

• Choosing $\mathcal{E}$: $$||x||^2 < 40960 \iff \frac{240}{k} \mathcal{E} < 40960 \iff \mathcal{E} < 2048$$ We chose $\mathcal{E} = 2025$.

• We have the following upper bound for a single chunk: $$p_e < \exp(-\frac{1}{8}(1-\frac{2\ln(2)}{A})^2Ak)$$. Therefore, by the union bound, we have the following upper bound for the whole message: $$\mathbb{P}_e \leq \frac{240}{k}\exp(-\frac{1}{8}(1-\frac{2\ln(2)}{A})^2Ak)$$. Plugging in our chosen values for $k$ and $\mathcal{E}$, we find $\mathbb{P}_e \leq 0.04$

How to run the code

You need to run the file full_design,py in order to run the code. Two command line arguments are required:

• --mode followed by the chosen mode (local, client or error_prob)
  • "local" mode is used to send a message on a simulated local channel.
  • "client" mode is used to send a message to the provided server.
  • "error_prob" mode is used to test the error probability of the channel(locally).
• --input_string followed by the message you want to send. If not provided, the default message is "saluttoutlemonde40charscestlaviehuhuhu12". Not required in the "error_prob" mode.

Examples :

1. python full_design.py --mode local --input_string "1234567890123456789012345678901234567890"
2. python full_design.py --mode client --input_string "1234567890123456789012345678901234567890"
3. python full_design.py --mode error_prob

Code structure

• transmitter.py : receives a message, encodes as described and outputs it to a file "client/transmitted_signal.txt" ("local/transmitted_signal.txt" in client mode). This file is then passed to the channel.
• receiver.py : receives the signal from the channel, decodes it and outputs the decoded message to a file "client/received_message.txt" ("local/received_message.txt" in client mode).
• full_design.py : main file that describes the full communication system i.e runs the transmitter, channel and receiver.