Network Information Theory (Channel Capacity)

Part 2

Muhammad Fahim Ul Haque Computer Engineering Division

EE Department Linköping University

Content of Presentation

• Multiple Access Channel (Continued) Gausian Multi Access Channel Gausian Channel Capacity for FDMA,TDMA &CDMA) m-user Multi Access Channel

• Broadcast Channel Degraded Broadcast Channel Capacity of Degraded Broadcast Channel Book Example Gausian Degraded Broadcast Channel

• Relay Channel

Gaussian Multiple Acces Channel

Gaussian Multiple Acces Channel

• Generalize case for capacity region for multiple acces channel is given as:

• Capacity region for gausian channel drived from above equation

(1)

(2)

(3)

Gaussian Multiple Acces Channel

From equation 1

-------------------------------(4)

---(5)

--------------------------(6)

----------------------------------(7)

---------------------------------------(8)

-----------(9)

-----------------------------------------(10)

Gaussian Multiple Acces Channel

----------------------(11)

(12)

----------------------------------(13)

--------------------------(14)

--------------------(15)

(16)

-------------------------(17)

Gaussian Multiple Acces Channel

• So

----------------------(18)

----------------------(19)

--------------(20)

Gaussian Multiple Acces Channel

• FDMA

• TDMA

• CDMA

m- user Channel

Broad Cast Channel

Examlpes Of Broadcast Channel

• TV Broadcast Station

• Class Room Lecture

• TV Broadcast Station(Simultanous HDTV and Regular Transmission)

• Orthogonal Broadcast Station.

Broadcast Channel

• A broadcast channel with two reciever of rate R1 and R2 and there is no common info. sent to both reciver

Broadcast Channel

• A rate (R1,R2) is said to be achivable for the broadcast channel if there exists a sequence of ((2nR1,2nR2),n) codes with

• The chanel where we have common info. Of rate R0 to be sent to both reciever.

0)( n

eP

Broadcast Channel

• A rate triple (R0,R1,R2) is said to achievable for broadcast channel with common info. If there exist a sequence of ((2nR0,2nR1,2nR2),n) codes with

• The capacity region of the broadcast channel is the closure

of the set of achievable rates. • Theorem 15.6.1: The capacity region of a broadcast

channel depends only on the conditional margional distributions p(y1|x) and p(y2|x).

0)( n

eP

Degraded Broadcast Channels

• A broad cast channel is said to be physically degrades if

• A broadcast channel is said to be stochastically degrade if its conditional margional distribution are same as that of physically degraded broadcast channel

Capacity of Degraded Broadcast Channel

Capacity of Degraded Broadcast Channel

• Proof

Capacity of Degraded BroadCast Channel

Broadcast Channel

Gaussian Broadcast Degraded Channel

Relay Channel

Relay Channel

Relay Channel

Relay Channel

Refrences

• Element of Information Theory (Second Edition) by Thomas M. Cover & Joy A. Thomas