Channel Lab

Data Communication, Lecture 3. Real channels weaken signals, add noise and take time. Change the numbers and watch what happens.

Power along the link · bars in mW

Add up the gains and losses

Total gain Output power P₂ Output in dBm

Decibels add: the total is just the sum of the three stages. Powers multiply: P₂ = P₁ × 10^(total/10).

Received signal = sent bits + noise · dashed line = decision threshold
Bits the receiver decides · orange = wrong

How much noise can the bits survive?

SNR as a ratio Bits in error

SNR_dB = 10 log₁₀(signal power / noise power). Every 10 dB down means ten times more noise relative to the signal.

Maximum data rate · Nyquist (blue, noiseless) vs Shannon (orange, the real limit)

How fast can this channel go?

Nyquist 2B log₂L Shannon B log₂(1+SNR) Useful levels at this SNR

Where the time goes · one message, end to end

Latency = propagation + transmission + queuing + processing

Propagation Transmission Total latency Bandwidth × delay

Try a 5,000 kB file at 1 Mbps: transmission time takes over. For a short message, distance dominates.