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S.72-227 Digital Communication Systems
Advanced Modulation and Random Access Techniques
2Timo O. Korhonen, HUT Communication Laboratory
Agenda today Review of code error detection and correction capability ARQ-techniques
– Stop-and-wait– go-back-N– Selective-repeat
ARQ throughput efficiency Selective-repeat in polar signaling AWGN channel Trellis coded modulation (TCM)
– set-partitioning– subset selection
Dynamic medium access Delay-bandwidth product Throughput
– ALOHA– Slotted ALOHA
3Timo O. Korhonen, HUT Communication Laboratory
4Timo O. Korhonen, HUT Communication Laboratory
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6Timo O. Korhonen, HUT Communication Laboratory
7Timo O. Korhonen, HUT Communication Laboratory
8Timo O. Korhonen, HUT Communication Laboratory
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11Timo O. Korhonen, HUT Communication Laboratory
Trellis coded modulation (TCM) [2-3]
In TCM modulation and coding are treated as
– a combined entity to
– maximize total effective Euclidean distance between
– mapped code paths in decoder state trellis. This is realized by
– Setting the number of points in constellation larger than required by the modulation format. Extra used to give space for redundancy required by error control
– Convolutional coding used to introduce dependency between constellation points such that only certain constellation patterns (sequences) allowed
– Soft-decision decoding is used at the receiver to get additional sensitivity gain of order of 2-3 dB
12Timo O. Korhonen, HUT Communication Laboratory
13Timo O. Korhonen, HUT Communication Laboratory
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15Timo O. Korhonen, HUT Communication Laboratory
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20Timo O. Korhonen, HUT Communication Laboratory
21Timo O. Korhonen, HUT Communication Laboratory
Poisson frequency distribution[1]
!(1) ( , , ) (1 )
!( )!k n k
bin
nP n k a a a
k n k
22Timo O. Korhonen, HUT Communication Laboratory
Poisson distribution - example [1]
For Poisson distribution we haveand therefore average number of errors is
and the probability frequency distribution function is
Cumulative distribution yields then required probability as
Checking with Mathematica yields:
2( ) , , (1 )!
im
I
mP i e m n m
i
4 510 5 10 0.5m n
0 1 20.5 0.5 0.5 0.5
(2) 0.9860! 1! 2!IF e
0.5 0.5( )
!
i
IP i ei
23Timo O. Korhonen, HUT Communication Laboratory
ALOHA’s throughput
The probability that the transmitted packet will not overlap with a another packet is the prob. that no packet is transmitted within the vulnerable period
Assuming that the offered mean traffic is 2G in 2X seconds (=vulnerable period) (X :time to transmit the frame) results that the probability of making k transmission within the vulnerable period is
Channel throughput S equals (offered traffic G)x(probability of successful transmission) or
0
P[no collisions within the vulnerable period]
(2 )exp( 2 ) exp( 2 )
0!
S G
GS G G G G
(2 )[ ] exp( 2 ), 0,1,2,...
!
kGP k G k
k
( : number of packets/sec)G X X=L/R L: frame length (bits)
24Timo O. Korhonen, HUT Communication Laboratory
Slotted-ALOHA (slot size = frame length)
0 ( 1)t k X exp( )S G G
ALOHA
S-ALOHA
1
exp( )S G G G
In the Slotted ALOHA-system transmission is allowed atyielding for throughput
Note that ALOHA yields maximumthroughput for G = 1/2, that means offering in average one frame within the vulnerable period (if more is offered, collision prob. increases)
However, if the offered traffic G is very small, actually almost all offered traffic goes through because then
offered traffic
throughput
25Timo O. Korhonen, HUT Communication Laboratory
References
[1] A.B. Carlson: Communication Systems (4th ed) [2] Haykin S: Communication Systems (3th ed) [3] J. G. Proakis: Digital Communications (4th ed) [4] Stallings W: Data and Computer Communications (7th ed) [5] M. Duck, R. Read: Data Communications and Computer Networks
(2th ed) [6] G. Ungerboeck: “Trellis-coded Modulation with Redundant Signal
Sets, Parts I and II, IEEE Communications Magazine, vol. 25, pp. 5-21, Feb. 1987
[7] A. Leon-Garcia, I. Widjaja: Communication Networks (2th ed)