Topic: Digital baseband communication (previously called pulse modulation)
Context: Form of digital communication, distinct from band pass or wireless communication
Upcoming Lectures: Digital baseband, band pass, and multiplexing
Last Lecture: Process of digitization (sampling, quantization, anti-aliasing filters, quantization error, non-linear quantization, compounding)
Key Terminologies
Digitization: Converting analog signals to digital by sampling and quantization
Baseband Communication: Digital communication typically over cables without a high frequency carrier
Band Pass (Wireless) Communication: Often involves a high frequency carrier
Pulse Modulation: After encoding, converting digital data into pulses for transmission
Importance of Cables in Internet Communication
Backbone of the Internet: Undersea fiber optic cables responsible for 99% of international data traffic
Historical Context: First undersea cable laid over 177 years ago
Modern Data Rates: New cables, like Maria cable, support up to 160 terabits per second
Repeaters on Cables: Used to regenerate signals and combat attenuation and interference
Pulse Code Modulation (PCM)
Sample Process: Analog signal -> Sampling -> Quantization -> Encoding -> Pulse Modulation
Types of Pulse Modulation:
Pulse Amplitude Modulation (PAM)
Pulse Width Modulation (PWM)
Pulse Position Modulation (PPM)
PCM: Digital communication where each sample is represented by n bits
Data Rate Formula:
$$ \text{Data Rate} = n \times F_s $$
where n = bits per sample, F_s = samples per second
Bandwidth Requirement: Half of the data rate
Calculation Examples
Example Problem: If we have 16 (L=16) levels,
$$ n = \log_2(16) = 4 $$.
Assume a sample rate, F_s, of 10kHz, the bit rate is
$$ 40,000 \text{ bits/second} $$
True/False Questions:
Does 16 levels require half the bandwidth of 32 levels? (False)
Does 16 levels require double the bandwidth of 17 levels? (False)
Line Coding
Unipolar vs Bipolar: Unipolar has two levels (0, high), Bipolar has three (low, 0, high)
Return to Zero (RZ) vs Non Return to Zero (NRZ): RZ returns to zero within a bit period; NRZ does not
Bandwidth Efficiency: NRZ can transmit 2 bits per second per Hertz whereas RZ transmits 1 bit per second per Hertz
Channel Capacity and Bottlenecks
Determining Factors: Slowest link in communication path is the bottleneck
Shannon-Hartley Theorem: Channel capacity C is given by
$$ C = B \log_2(1 + S/N) $$
where B = bandwidth, S/N = signal-to-noise ratio
Examples of Bandwidth Calculation
Example Problem: Required data rate = 2.3 Mbps, SNR=70dB
Convert SNR from dB to power ratio:
$$10^{(70/10)} = 10^7 $$