Physical Layer: Encoding and Multiplexing

The physical layer moves raw bits over a wire, fibre or radio channel. It decides how a 0 and a 1 look as a signal, how fast bits can be sent, and how several signals share one medium.

Transmission media

Data rate limits

• Bit rate = bits per second; baud rate = signal changes (symbols) per second. With L signal levels, each symbol carries log₂ L bits: bit rate = baud × log₂ L.
• Nyquist (noiseless channel): maximum bit rate = 2 B log₂ L (B = bandwidth in Hz).
• Shannon (noisy channel): capacity C = B log₂(1 + S/N), whatever the number of levels. SNR in dB = 10 log₁₀(S/N).
• Use Shannon for the upper limit, then Nyquist for the number of levels needed.

Line coding

Line coding maps bits to voltage levels:

Block codes such as 4B/5B and 8B/10B add extra bits to guarantee enough transitions.

bits = "1011001"
nrz_l = "".join("+" if b == "1" else "-" for b in bits)

level, nrz_i = "-", ""
for b in bits:                          # NRZ-I: a 1 flips the level
    if b == "1":
        level = "+" if level == "-" else "-"
    nrz_i += level

manchester = " ".join("-+" if b == "1" else "+-" for b in bits)   # IEEE 802.3
print("NRZ-L     ", nrz_l)
print("NRZ-I     ", nrz_i)
print("Manchester", manchester)

NRZ-L      +-++--+
NRZ-I      ++-+++-
Manchester -+ +- -+ -+ +- +- -+

Modulation

To send digital data over an analog (band-pass) channel, a carrier is modulated: ASK (amplitude), FSK (frequency), PSK (phase) and QAM (amplitude and phase together; 16-QAM carries 4 bits per symbol).

Multiplexing

T1 line: 24 voice channels × 8 bits + 1 framing bit = 193 bits per frame, 8000 frames per second = 1.544 Mbps.

GATE-style practice questions