Network Information Theory (Channel Capacity) Part 2 · Broadcast Channel •A rate triple (R 0,R...
Transcript of Network Information Theory (Channel Capacity) Part 2 · Broadcast Channel •A rate triple (R 0,R...
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Network Information Theory (Channel Capacity)
Part 2
Muhammad Fahim Ul Haque Computer Engineering Division
EE Department Linköping University
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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
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Gaussian Multiple Acces Channel
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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)
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Gaussian Multiple Acces Channel
From equation 1
-------------------------------(4)
---(5)
--------------------------(6)
----------------------------------(7)
---------------------------------------(8)
-----------(9)
-----------------------------------------(10)
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Gaussian Multiple Acces Channel
----------------------(11)
(12)
----------------------------------(13)
--------------------------(14)
--------------------(15)
(16)
-------------------------(17)
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Gaussian Multiple Acces Channel
• So
----------------------(18)
----------------------(19)
--------------(20)
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Gaussian Multiple Acces Channel
• FDMA
• TDMA
• CDMA
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m- user Channel
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Broad Cast Channel
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Examlpes Of Broadcast Channel
• TV Broadcast Station
• Class Room Lecture
• TV Broadcast Station(Simultanous HDTV and Regular Transmission)
• Orthogonal Broadcast Station.
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Broadcast Channel
• A broadcast channel with two reciever of rate R1 and R2 and there is no common info. sent to both reciver
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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
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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
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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
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Capacity of Degraded Broadcast Channel
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Capacity of Degraded Broadcast Channel
• Proof
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Capacity of Degraded BroadCast Channel
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Broadcast Channel
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Gaussian Broadcast Degraded Channel
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Relay Channel
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Relay Channel
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Relay Channel
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Relay Channel
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Refrences
• Element of Information Theory (Second Edition) by Thomas M. Cover & Joy A. Thomas