Summary of Basic Concepts Sender Channel Receiver Dr. Christian - - PowerPoint PPT Presentation

Communications Research Group

Summary of Basic Concepts

• Dr. Christian Rohner

Transmission

Sender Receiver Channel

Encoding Modulation Demodulation Decoding

Noise

Symbols Bits

Terminology

• Bandwidth [Hz]
• range of frequencies that pass through a medium with

minimum attenuation.

• this is a physical property of the medium.
• Symbol rate [symbols/s; samples/s; baud]
• rate at which symbols (samples) are sent
• at most 2B symbols/s (B: Bandwidth of the channel [Hz])
• Data rate [bit/s]
• amount of bits sent over the channel per second.
• equal to number of symbols/s times bits/symbol.
• 1 kbit/s = 1000 bit/s (but: 1 kByte = 2^10 Byte = 1024 Byte)

Fourier Analysis

f(x) = 1 2a0 +

∞

• n=1

an cos(nπ T x) +

∞

• n=1

bn sin(nπ T x)

an = 1 T

2T

f(t)cos(nπ T x)dx bn = 1 T

2T

f(t)sin(nπ T x)dx a0 = 1 T

2T

f(t)dx

Channel Capacity

• Henry Nyquist 1924: even a perfect channel has a

finite transmission capacity:

B: bandwidth [Hz], V: discrete levels of signal

• Hartley-Shannon: upper bound for a noisy channel:
• Capacity [bit/s] is not Bandwidth [Hz]!

Rmax = 2B log2 V bit/s

Rmax = B log2(1 + S/N) bit/s

Noisy Channel Coding Theorem

• Can we send faster than the channel capacity?
• R < C
• there exists a coding technique which allows the probability
• r error at the receiver to be made arbitrarily small.
• R > C
• the probability or error at the receiver increases without

bound as the rate is increased.

• No useful information can be transmitted beyond the channel

capacity.

Block Error Rate

Example Block error rate p

Message of S bits

ǫ =P(bit error) P(no errors in S bits)= (1 − ǫ)S P(one or more errors in S bits)= p = 1 − (1 − ǫ)S = 10− = 1000

P(one or more errors in S bits)= ǫ = 10−3, S = 1000 p = 1 − (1 − 10−3)1000 = 0.63

Block Error Rate

1e-6 1e-5 1e-4 1e-3 1e-2 1e-0 1e-1 1e-0 1e-1 1e-2 S=100 S=1000 S=10000

bit error probability block error probability

Error Detection

• Known message Space
• Parity Check
• XOR over all data bits, add it to the message.
• Block sum check
• n blocks of m bits (i.e., n x m array)
• parity for every row, and every column
• Cyclic redundancy check (CRC)
• designed to detect error bursts
• polynomial code
• a generator polynomial of R bits will detect all single-bit

errors, all double-bit errors, all odd number of bit errors, all error bursts < R, most error bursts R.

Error Detection Two-dimensional Parity Example Checksum

• UDP Message:

011001100110000001010101010101011000111100001100

0110011001100000 0101010101010101 1000111100001100 0110011001100000 0101010101010101 1000111100001100 Transmitted Data: Check:

1s compl

Example CRC - Computation

Generator G=1001 Message D=101110 1001 101110000

G : D!2^3 = R=

Example CRC - Verification

Generator G=1001 Message D=101110 1001 101110011

G : D!2^3 ⊕ R =

Transmitted 101110011

Check:

Shared Medium

• Links are only seldom point-to-point...
• Ethernet
• Wireless (Wifi, Bluetooth, GSM, etc.)

Hidden node, exposed node

• Multiple Access:
• TDMA, FDMA, CDMA
• statistical multiplexing: CSMA, CSMA/CD, ALOHA, etc.
• Problem 1: Collisions, Errors
• Problem 2: Delay to get access to the medium

Network Model

Sender Receiver Network Node:

• Queue

Network Model

• Problem: Congestion due to high traffic load. Result: Delay
• Problem: Loss due to full queues.

...