Digital Communication Basics

Why it matters

Digital communication represents information as symbols sent through a physical channel. The transmitter maps bits to a waveform; the receiver estimates the symbols despite noise, interference and channel distortion.

Signal chain

A typical chain includes source encoding, channel encoding, symbol mapping, pulse shaping, modulation, the channel, receive filtering, synchronization, detection and decoding. Source coding reduces representation redundancy; channel coding adds structured redundancy for reliability. The two serve different purposes.

Rates and modulation

For fixed-length M-ary symbols carrying log2(M) bits each, uncoded bit rate R_b = R_s log2(M). Symbol rate R_s is in baud and bit rate in bit/s. With channel-code rate r = k/n, information rate is r times coded bit rate before other overhead.

BPSK has two phase states and carries one coded bit per symbol; QPSK has four states and carries two. QAM uses amplitude and phase. Higher M packs more bits per symbol but generally needs a higher signal-to-noise ratio for a given error probability.

For raised-cosine pulse shaping with roll-off α, the ideal baseband one-sided bandwidth is (1+α)R_s/2. The corresponding real passband occupied bandwidth is approximately (1+α)R_s. Always state the bandwidth convention.

Worked example

A QPSK link sends symbols at 100 kbaud with code rate 3/4 and roll-off 0.25. Ignore framing and pilot overhead.

Coded bit rate = 100000 × log2(4) = 200000 bit/s. Information bit rate = (3/4) × 200000 = 150000 bit/s. Symbol period = 1/100000 = 10 μs. Ideal passband bandwidth = 1.25 × 100000 = 125 kHz; one-sided baseband bandwidth is 62.5 kHz.

Noise and errors

Bit error rate is erroneous received bits divided by compared transmitted bits. Symbol error rate counts symbols, so it is not generally identical to BER. For coherent BPSK in additive white Gaussian noise with ideal synchronization, P_b = Q(√(2E_b/N_0)). This formula does not apply unchanged to arbitrary fading or interference channels.

Common mistakes

Equating baud with bit rate for every modulation; ignoring code rate; mixing one-sided baseband and passband bandwidth; assuming coding removes all errors; or substituting SNR for E_b/N_0 without accounting for rate and bandwidth.

Quick check

1. How many bits does a QPSK symbol represent?
2. What does a rate-1/2 code do to 100 kbit/s information before modulation, ignoring overhead?
3. Is a 10 kbaud 16-QAM stream 10 kbit/s?

Answers: 1. Two coded bits. 2. Produces 200 kbit/s coded data. 3. No, it carries 40 kbit/s before coding/overhead adjustments.