Cooperative Strategies and Capacity Theorems for Relay Networks

Transcription

1 بسم الرحمن الرحيم King Fahd University of Petroleum and Minerals College of Engineering Sciences Department of Electrical Engineering Graduate Program Cooperative Strategies and Capacity Theorems for Relay Networks By: Anas (M.A.) Ata Salhab. Supervised by: Dr. Samir Al-Ghadhban. Course: Information Theory. June, 2010

2 1 Introduction. Models and preliminaries. Wireline strategies. Wireless models. Numerical results of related work. Comments.

3 2 The area of relay networks is a very hot area of research in both wireline and wireless communications. The Technique: source intermediate nodes destination Advantages: - Achieving broader coverage without the need for a high power transmitter.

4 3 - Mitigating fading. - Providing spatial diversity (cooperative comm.). - Also, cooperation in wireline networks as in multiaccess relay channels (MARCs). Applications: - It is used to communicate via add hoc networks where nodes are communicating without the aid of central control/infrastructure [1]. - Recently, this technique has gained new actuality in collaborative/cooperative wireless communication systems [2].

5 4 Two main schemes: - Decode-and-forward (DAF). - Compress-and-forward (CAF). The DAF strategies have as a common feature that the source controls what the relays transmit. For wireless networks, one consequently achieves gains related to multiantenna transmission. In the CAF strategy, the relay forwards a quantized and compresses version of its channel outputs to the destination.

6 5 Relay network model: (a) (b) Figure 1: Model of relay networks: (a) 1-relay network; (b) 2-relay network.

7 6 Used parameters: - The previous Figure gives two different relay networks, T = 3 and T = 4. - T 2 relays (nodes t with t { 2, 3,, T 1} ). W - is the message. X, t = 1, 2,, T 1, i = 1, 2,, N, - ti are the channel inputs. - Y, t = 2,, T, i = 1, 2,, N, are the channel outputs. ti Wˆ - is the message estimate.

8 7 - The channel will be assumed memoryless timeinvariant channel. - The channel distribution can be given by: ( ) 2 T 1 T 1 p y,, y x,, x (1) - For example: the T = 3 network (wired) [ ] Channel inputs: X = X, X and Y 2 X 2 [ ] Channel outputs: and Y = Y, Y

9 8 - The channel distribution for this case is: ( ) = ( 2 11) ( ) ( 32 2 ) p y, y x, x p y x p y x p y x (2) Capacity upper bound: { } - Let X S X t : t S and T = 2, 3,, T 1. A capacity upper bound is given in [3] as: = { } C max min I X X ; Y Y X (3) ( ) 1 S T (,,, ) S T S S p x x x 1 2 T 1 where C S is the complement of S in T. C C

10 9 - Example: for T = 3 For this case, we have: X 1 form the source. T = { 2}. S = { φ, 2}. { } C max min I X ; Y Y X, I X X ; Y (4) ( ) ( ) (, x ) p x 1 2 { } C min C + C, C + C (5)

11 10 MARC Model: - The model is shown in next Figure: - Node 1 and 2 transmit the ind. messages W1 and W2 with rates R1 and R2 - Three inputs and 2 outputs. Figure 2: A MARC with two sources.

12 11 - Inputs: [, ] X = X X [, ] X = X X X 3 - Outputs: [, ] Y = Y Y [,, ] Y = Y Y Y

13 12 - The channel distribution is: ( 3, 4 1, 2, 3 ) = ( 31 11) ( 32 21) p ( y 41 x 12 ) p ( y 42 x 22 ) p ( y 43 x 3 ) p y y x x x p y x p y x (6)

14 13 Decode-and and-forward: - From [4], the rates for one relay is given by: { } R = max min I X ; Y X, I X X ; Y (7) DF ( ) ( ) (, x ) p x 1 2 { } C = min C, C + C (8) { } C max min I X ; Y Y X, I X X ; Y (9) ( ) ( ) (, x ) p x 1 2 { } C min C + C, C + C (10)

15 14 - Regular encoding for one relay: 1. The message w is divided into B blocks of length nr each. 2. The transmission is performed in B+1 blocks by transmitting codewords of length n. 3. Node 1 transmits x 1 i, j and node 2 transmits x 2 ( j ). 4. Quantities: W ( ) =, = ( + 1 ), and R = R B / ( B + 1) B BnR N B n W

16 15 - The DAF model and the information transfer are shown in Figures below: Figure 3: DAF for one relay. Figure 4: The information transfer for regular encoding/sliding window decoding.

17 16 - Strategy steps: 1. In the1 st block: node 1 and 2 transmit their codewords. 2. Node will reliably decode w1 if n is large and: 3. In the 2 nd block. ( ) R < I X ; Y X (11) 4. Finally, depending on the used decoding strategy:

18 17 - If the backward decoding is used: y 3b a. Let be the bth block of channel outputs of node 3. b. At block b+1, we have y 3( b + 1) and all the previous outputs (stored). c. Now, node 3 can decode w b reliably if n is large and: R < I X X ; Y (12) ( ) d. One continues in this fashion until all message blocks have been decoded.

19 18 e. To have a rate close to R, one may use large number of blocks: ( ) R = R B / B + 1 W - Using the sliding window decoding: At node 3: after receiving y 3b, b 3, it similarly decodes w b by using y 1 3( b 1) and y 3b, all the while (3) assuming its past message estimate is. wˆ b 2 w b 2

20 19 No fading and one relay: Figure 5: A single relay on a line.

21 20 Special case 1: d 0 Special case 2: d 1

22 21 Curve for one relay: P1 = P2 = 10, alpha =2: Figure 6: Rates for one relay.

23 22 1) 1) Pout out vs. normalized SNR: Comparison of Outage Probability for Regenerative and Non-Regenerative Systems 10 0 Outage Probability Pout Non-Regenerative System - Balanced Regenerative System - Balanced Non-Regenerative System - Un-Balanced Regenerative System - Un-Balanced Normalized SNR [db] Figure 7: Comparison of Pout of reg. and non-reg. systems.

24 23 2) BER vs. average SNR per hop: of Bit Error Rates for Regenerative and Non-Regenerative Systems 0Comparison 10 Non-Regenerative System Regenerative System Bit Error Rate Pb(E) Average SNR per Hop [db] Figure 8: Comparison of the BER of reg. and non-reg. systems (balanced).

25 24 This paper gives many basic theorems and relations of channel capacity and system rates for both wireline and wireless system. Various schemes were presented and compared in this work: DAF, CAF, MARC and BRC channels, single and multi relays. Other parts of the papers dealt with the effect of antenna on the wireless systems and the fading.

26 25 1. Mazen O. Hasna and Mohamed-Slim Alouini, Average Outage Duration of Multihop Communication Systems With Regenerative Relays, IEEE Transactions on Wireless Communications, vol. 4, no. 4, pp , July J. N. Laneman and G. W. Wornell, Energy efficient antenna sharing and relaying for wireless networks, in Proc. IEEE Wireless Communications and Networking Conf. (WCNC 00), Chicago, IL, Oct. 2000, pp M. R. Aref, Information flow in relay networks, Ph.D. dissertation, Stanford Univ., Stanford, CA, Oct T. M. Cover and A. A. El Gamal, Capacity theorems for the relay channel, IEEE Trans. Inf. Theory, vol. IT-25, no. 5, pp , Sep. Anas (M.A.) Salhab Information Theory

27 26 Any questions?? Anas