1. Link Layer; Media Access Control
Y. Richard Yang
1/27/2009

2. Outline
Admin. and recap
Intro to link layer
Media access control

3. Admin. Office hours posted on course information page
Any questions on hw 1?

4. Recap: ISI ISI: one symbol spreads to other symbols
e.g., each symbol is 1 ms
delay spread is 3 ms
then one symbol spreads to 3 symbols
Solution techniques
extract the symbols despite ISI: equalization
reduce symbol rate: OFDM

5. Recap: Equalization
Problem: given received y sequence, determine the most likely transmitted x sequence (maximum likelihood detection):
Using Viterbi algorithm to identify the x sequence effectively
Maximum likelihood detection is commonly used in communications and networks
y[1] = x[1] h0 + w[1] y[2] = x[2]h0 + x[1] h1 + w[2] y[3] = x[3]h0 + x[2]h1 + x[3] h2 + w[3] y[4] = x[4]h0 + x[3]h1 + x[2] h2 + w[4] y[5] = x[5]h0 + x[4]h1 + x[3] h2 + w[5] … y[L] = x[L]h0 + x[L-1]h1 + x[L-2]h2 + w[L] y[L+1] = x[L]h1 + x[L-1]h2 + w[L+1] y[L+2] = x[L]h2 + w[L+2]

6. Recap: Orthogonal Frequency Division Multiplexing (OFDM)
Uses multiple carriers modulation (MCM)
each subcarrier uses a low symbol rate
reduce symbol rate and reduce ISI
for N parallel subcarriers, the symbol time can be N times longer
spread symbols across multiple subcarriers
also gains frequency diversity
Uses orthogonal frequencies to avoid large guard band
if frequencies are chosen so that an integral number of cycles in a symbol period, they are orthogonal

7. OFDM Encoding/Decoding (BPSK)
During one symbol time, we transmit at N subcarriers
Example: how the receiver recovers x1(t):
it computes correlation between y(t) and sin(2f1t)
fsymbol=1/T

8. OFDM Decoding fsymbol=1/T Assume f1 = 1671 fsymbol, f2 = 1672 fsymbol
sin(a)sin(b) = ½(cos(a-b)-cos(a+b))
OFDM Decoding
consider
fsymbol=1/T
Assume f1 = 1671 fsymbol, f2 = 1672 fsymbol

9. Example: 802.11a OFDM fsymbol = 312.5 KHz (symbol time?)
N = 64 (useful N = 52)
312.5 * 64 = 20 MHz
Channel 40 : [5.200 – 5.220] GHz
Can a OFDM have a subcarrier at GHz?
Channel 44 : [5.220 – 5.240] GHz

10. OFDM Implementation: FFT
channel

11. Outline
Recap
Introduction to link layer

12. Link Layer Services Framing: Flow control:
encapsulate bits into frame, adding header, trailer
multiplexing: frame header to identify source, dest
example: MAC address
error detection and correction
Flow control:
pacing between adjacent sending and receiving nodes
Link access (interference and quality of service control)
media access control (also called multiplexing)

13. Outline Recap Introduction to link layer
Error detection and correction

14. Reed-Solomon Codes
Very commonly used, send n symbols for k data symbols
e.g., n = 255, k = 223
We will discuss the original version (1960)
modern versions are slightly different; they use generator polynomial, but the idea is essentially the same
If the data we want to send is (x0, x1,…, xk-1), where xi are data symbols, define polynomial P(t) = x0 + x1t + x2t + …xk-1tk-1
Assume  is a generator of the symbol field (i.e., i not equal to j if i not equal to j)
Then for the data sequence, send
P(0), P(), P(2), P(n-1) to receiver

15. since any k equations are independent, they have a unique solution
Reed-Solomon Codes
Receive the message P(0), P(), P(2), P(n-1)
If no error, can recover data from any k equations:
since any k equations are independent, they have a unique solution

16. Reed-Solomon Codes: Handling Errors
But, what if s errors occur during transmission?
Keep a counter (vote) for each solution
Enumerate all combinations of k equations, for each combination, solve it, and increase the counter of the solution
Identify the solution which gets the largest # of “votes”

17. Reed-Solomon Codes
The transmitted data is the correct solution for n-s equations, and thus gets
votes (i.e., combinations of k equations)
An incorrect solution can satisfy at most k-1+s equations, and the # of votes it can get is at most:

18. Reed-Solomon Codes If
or (n-s > k – 1 + s) or (n-k > 2s – 1) or (n-k  s), it can correct any s errors

19. Reed-Solomon Codes
The voting-based decoding algorithm proposed in 1960 is inefficient
Berlekamp introduced first truly efficient algorithm for both binary and nonbinary codes. Complexity increases linearly with number of errors
Sugiyama, et al. Showed that Euclid’s algorithm can be used to decode R-S codes
Below is a typical current decoder

20. Outline Recap Introduction to link layer
Error detection and correction
Media access control

21. Dimension for multiplexing
Multiple Access Control
Dimension for multiplexing
Frequency
Time
Space
Code
Two transmissions cannot conflict in all dimensions !

22. FDMA FDMA: frequency division multiple access
Channel divided into frequency bands
A transmission uses a frequency band
frequency bands
time 5 1 4 3 2 6

23. TDMA TDMA: time division multiple access
Time divides into frames; frame divides into slots
A transmission uses a slot in a frame

24. Q: why not divide into infinite small cells?
SDMA
SDMA: space division multiple access
Transmissions at different locations, if far enough, can transmit simultaneously (same freq.)
Example: the cellular technique 1 2 3 4
Suppose 24 MHz spectrum, 30 K per user
#user supported: =
Using cell #user supported: =
Q: why not divide into infinite small cells?

25. CDMA CDMA (Code Division Multiple Access)
Unique “code” assigned to each user; i.e., code set partitioning
All transmissions share the same frequency and time; each transmission uses DSSS, and has its own “chipping” sequence (i.e., code) to encode data
e.g. code =
Examples: Sprint and Verizon, 3G WCDMA and CDMA2000

26. DSSS Revisited tb: bit period tc: chip period tb user data d(t) 1 -1 X
code c(t) -1 1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 =
resulting
signal -1 1 1 -1 1 -1 1 1 -1 -1 1 -1 1 -1
tb: bit period
tc: chip period

27. Illustration: CDMA/DSSS Using BPSK
Assume BPSK modulation using carrier frequency f :
yi(t) = A xi(t)ci(t) sin(2 ft)
A: amplitude of signal
f: carrier frequency
xi(t): data of user i in [+1, -1]
ci(t): code of i (a chipping sequence in [+1, -1])
Suppose only i transmits
y(t) = yi(t)
Decode at receiver i
incoming signal multiplied by ci(t) sin(2 ft)
since, ci(t) ci(t) = 1, yi(t)ci(t) sin(2 ft) = A xi(t) sin2(2ft)

28. Illustration: Multiple User CDMA
Assume M users simultaneously transmit: y(t) = y1(t) + y2(t) … + yM(t)
At receiver i, incoming signal y(t) multiplied by ci(t) sin(2 ft)
consider the effect of j’s transmission
yj(t)ci(t) sin(2 ft) = A cj(t)ci(t)xj(t) sin2(2 fct)

29. CDMA: Deal with Multiple-User Interference
Two codes Ci and Cj are orthogonal, if
, where we use “.” to denote inner product, e.g.
If codes are orthogonal, multiple users can “coexist” and transmit simultaneously with minimal interference
C1:
C2:
C1 . C2 = (-1) (-1) (-1)+(-1)=0
Analogy: Speak in different languages!

30. Capacity of CDMA B
In realistic setup, cancellation of others’ transmission is incomplete
Assume the received power at base station from all nodes is the same P (how?)
The power of the transmission with known code is increased to N P, where N is chipping expansion factor
The others remain on the order of P
Assume a total of M users
Then
For IS-95 CDMA, N = 1.25M/4800 = 260

31. Generating Orthogonal Codes
The most commonly used orthogonal codes in current CDMA implementation are the Walsh Codes
Property of Walsh : every row is orthogonal to every other row and the log NOT of every other row

32. Walsh CDMA Code Assignment
1,1,1,1,1,1,1,1
1,1,1,1
...
1,1,1,1,-1,-1,-1,-1
1,1
1,1,-1,-1,1,1,-1,-1
...
1,1,-1,-1
X,X
1,1,-1,-1,-1,-1,1,1 1 X
1,-1,1,-1,1,-1,1,-1
X,-X
...
1,-1,1,-1
1,-1,1,-1,-1,1,-1,1
1,-1 n 2n
1,-1,-1,1,1,-1,-1,1
...
1,-1,-1,1
1,-1,-1,1,-1,1,1,-1 1 2 4 8
If user 1 is given code [1,1,-1,-1], what codes can we give to other users?

33. WCDMA Orthognal Variable Spreading Factor (OSVF)
Flexible code (spreading factor) allocation
up link SF: 4 – 256
down link SF:
1,1,1,1,1,1,1,1
1,1,1,1
...
1,1,1,1,-1,-1,-1,-1
1,1
1,1,-1,-1,1,1,-1,-1
...
1,1,-1,-1
X,X
1,1,-1,-1,-1,-1,1,1 1 X
1,-1,1,-1,1,-1,1,-1
X,-X
...
No parent-child on the code tree
1,-1,1,-1
1,-1,1,-1,-1,1,-1,1
1,-1
SF=n
SF=2n
1,-1,-1,1,1,-1,-1,1
...
1,-1,-1,1
1,-1,-1,1,-1,1,1,-1
SF=1
SF=2
SF=4
SF=8

34. W-CDMA Down Link Capacity

35. Summary
SDMA, TDMA, FDMA and CDMA are basic media partitioning techniques
divide media into smaller “pieces” (space, time slots, frequencies, codes) for multiple transmissions to share
A remaining question is: how does a network allocate space/time/freq/code?

36. General Allocation Problem
Each transmission i (si->di) is specified by
transmission power pi
time ti
frequency band fi
code ci
Given any two transmissions (si->di; pi, ti, fi, ci) and (sj->dj; pj, tj, fj, cj), we can determine if they conflict
MAC scheduling problem:
to maximize resource efficiency
to allocate resource fairly
to satisfy app requirements
e.g. real time app (such as VoIP) need access with a bounded delay
e.g. s wants to talk to d, but cannot reach d directly

37. MAC The general case is challenging and largely still open
We start with the simplest scenario (e.g., or cellular up links) in this class:
time sharing the same frequency and code
a single receiver (the Access Point)

38. How to do Time Sharing? Fixed allocation
Centralized authority, e.g., polling
Taking turns, e.g., token passing
Distributed random access
discussion: compare the schemes in terms of
efficient utilization of resources
delay to access channel
quality of service (e.g., a guaranteed rate)

39. Pros and cons of slotted Aloha?
Random Access: Slotted Aloha B
Time divided into slots
get a frame
repeat:
at each slot transmit with probability p;
until no collision A B C E S
Pros: simple
Cons: clock sync; low efficiency
Used in GSM initial access channel
How big should a slot be?
Pros and cons of slotted Aloha?

40. Pros and Cons of Slotted Aloha
Pros: simple
Cons:
need clock sync
low efficiency: utilization at ~1/e

41. Backup Slides

42. Forward Error Correction Code: Block Erasure Code
Basic idea: encode k symbols to n symbols so that if the receiver receives any k symbols, it can recover the original x y

43. FEC/Block: Example Implementation
Suppose data signal is x, and the encoded signal y = Gx, where G is the generator matrix; assume receives only a subset of y
The y-symbols in yellow are received;
other y-symbols are dropped by demodulator

44. FEC: An Example using Vandermonde Matrix
Suppose gij are the entries after the identify matrix
gij= aij-1, where ai are distinct numbers
Suppose k=3, and n=5

45. An Example using Vandermonde Matrix
Suppose y2 and y3 are dropped, then we have y1, y4, and y5. Given the relationship (we know they are y1, y4, y5)
Since the matrix is not singular, we can recover x1, x2, and x3 from y1, y4, y5

46. Other Codes
Many other types of codes are commonly used in networks, e.g., Reed-Solomon codes
where we consider each symbol (e.g., 8 bits) as the coefficient of a polynomial, c(x) is the parity check polynomial representing the parity correction symbols, d(x) the data polynomial, and g(x) the generator polynomial in the format:

47. CSMA + Exponential Backoff + RTS/CTS/DATA/ACK
Summary
Use RTS/CTS for virtual carrier sense
Use ACK to improve reliability
Missing CTS/ACK triggers exponential backoff
Protocol
begin:
while (channel busy) wait
if channel idle
send RTS
if receive CTS
send DATA
wait for ACK
if ACK
return
exponential backoff
wait for the backoff period
goto begin;