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

Transmission Summary of Basic Concepts Sender Channel Receiver Dr. Christian Rohner Encoding Modulation Demodulation Decoding Bits Symbols Noise Communications Research Group Terminology Fourier Analysis • Bandwidth [Hz] - range of frequencies that pass through a medium with ∞ ∞ f ( x ) = 1 a n cos( n π b n sin( n π � � minimum attenuation. 2 a 0 + T x ) + T x ) - this is a physical property of the medium. n =1 n =1 • Symbol rate [symbols/s; samples/s; baud] - rate at which symbols (samples) are sent � 2 T - at most 2B symbols/s (B: Bandwidth of the channel [Hz]) a 0 = 1 f ( t ) dx • Data rate [bit/s] T 0 - amount of bits sent over the channel per second. - equal to number of symbols/s times bits/symbol. � 2 T a n = 1 f ( t ) cos ( n π - 1 kbit/s = 1000 bit/s (but: 1 kByte = 2^10 Byte = 1024 Byte) T x ) dx T 0 � 2 T b n = 1 f ( t ) sin ( n π T x ) dx T 0

Channel Capacity Noisy Channel Coding Theorem • Henry Nyquist 1924: even a perfect channel has a • Can we send faster than the channel capacity? finite transmission capacity: • R < C B: bandwidth [Hz], V: discrete levels of signal - there exists a coding technique which allows the probability R max = 2 B log 2 V bit/s or error at the receiver to be made arbitrarily small. • Hartley-Shannon: upper bound for a noisy channel: • R > C - the probability or error at the receiver increases without R max = B log 2 (1 + S/N ) bit/s bound as the rate is increased. - No useful information can be transmitted beyond the channel capacity. • Capacity [bit/s] is not Bandwidth [Hz]! Block Error Rate Block Error Rate 1e-0 Message of S bits block error probability Block error rate p 1e-1 ǫ =P(bit error) S=10000 P(no errors in S bits)= (1 − ǫ ) S P(one or more errors in S bits)= p = 1 − (1 − ǫ ) S S=1000 = 10 − = 1000 S=100 Example 1e-2 P(one or more errors in S bits)= ǫ = 10 − 3 , S = 1000 p = 1 − (1 − 10 − 3 ) 1000 = 0 . 63 1e-6 1e-5 1e-4 1e-3 1e-2 1e-1 1e-0 bit error probability

Error Detection 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. Two-dimensional Parity Example Checksum • UDP Message: 011001100110000001010101010101011000111100001100 0110011001100000 Transmitted Data: 0101010101010101 0110011001100000 0101010101010101 1000111100001100 1000111100001100 1s compl Check:

Example CRC - Computation Example CRC - Verification Generator �� G=1001 Generator �� G=1001 Transmitted 101110011 Message �� � D=101110 Message �� � D=101110 D ! 2^3 : G = D ! 2^3 ⊕ R : G = 101110000 1001 101110011 1001 R= Check: Shared Medium Network Model • 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. Sender Network Node: Receiver • Problem 1: Collisions, Errors - Queue • Problem 2: Delay to get access to the medium

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