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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

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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

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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)