State of the Cognitive Interference Channel

Transcription

1 State of the Cognitive Interference Channel Stefano Rini, Ph.D. candidate, Daniela Tuninetti, Natasha Devroye,

2 Interference channel Tx 1

3 DM Cognitive interference channel Tx 1 Gaussian Cognitive interference channel b a 3!4)**+,-.*5)*0121!"#$%&'()**+,-.*/)*0121

4 Contributions Tx 1 new inner bound (largest region) new outer bound (not tightest, but computable) capacity for deterministic channels (also semi-deterministic) 1.8 bit gap result for Gaussian channels (preliminary simulations show smaller gap)

5 Introduction N. Devroye, P. Mitran, and V. Tarokh, Achievable rates in cognitive radio channels, in 39th Annual Conf. on Information Sciences and Systems (CISS), Mar , Achievable rates in cognitive radio channels, IEEE Trans. Inf. Theory, vol. 52, no. 5, pp , May N. Devroye, Information theoretic limits of cognition and cooperation in wireless networks, Ph.D. dissertation, Harvard University, S. Gel fand and M. Pinsker, Coding for channel with random parameters, Problems of control and information theory, Capacity in very weak interference vol. 54, no. 10, pp , Oct A. Jovicic and P. Viswanath, Cognitive radio: An information-theoretic perspective, Proc. IEEE Int. Symp. Inf. Theory, pp , July G. Kramer, Topics in Multi-User Information Theory, ser. Foundations and Trends in Communications and Information Theory. Vol. 4: No 45, pp W. Wu, S. Vishwanath, and A. Arapostathis, Capacity of a class of cognitive radio channels: Interference channels with degraded message se Information Theory, IEEE Transactions on, vol. 53, no. 11, pp , Nov Capacity in very strong interference I. Maric, R. D. Yates, and G. Kramer, Capacity of Interference Channels With Partial Transmitter Cooperation, IEEE Trans. Inf. Theory, vol. 53, no. 10, pp , Oct Large unified region I. Maric, A. Goldsmith, G. Kramer, and S. Shamai, On the capacity of interference channels with a cognitive transmitter, European Transactions on Telecommunications, vol. 19, pp , Apr I. Maric, R. Yates, and G. Kramer, The capacity region of the strong interference channel with common information, in Signals, Systems and Computers, Broadcast channel is contained 2007 IEEE Information Theory Workshop on, July 2007, pp Y. Cao and B. Chen, Interference channel with one cognitive transmitter, in Asilomar Conference on Signals, Systems, and Computers, Oc, Interference Channels with One Cognitive Transmitter, Arxiv preprint arxiv: v1, T. Cover and J. Thomas, Elements of Information Theory. Wiley-Interscience, Special case of broadcast channel with cognitive radios no. 10, pp , Oct J. Jiang, I. Maric, A. Goldsmith and S. Cui, Achievable Rate Regions for Broadcast Channels with Cognitive Radios, IEEE Information Theory Workshop (ITW), Taormina, Italy, Oct Tx 1

6 Causal cognitive interference channel S. H. Seyedmehdi, Y. Xin, J. Jiang, and X. Wang, An improved achievable rate region for the causal cognitive radio, in Proc. IEEE Int. Symp. Inf. Theory, June Previous talk: S. I. Bross, Y. Steinberg, and S. Tinguely, ``The Causal Cognitive Interference Channelʼʼ Semi-deterministic cognitive interference channel Y. Cao and B. Chen, Interference channel with one cognitive transmitter, in Asilomar Conference on Signals, Systems, and Computers, Oct , Interference Channels with One Cognitive Transmitter, Arxiv preprint arxiv: v1, Cognitive interference channels with secrecy O. Simeone and A. Yener, The cognitive multiple access wire-tap channel, in Proc. Conf. on Information Sciences and Systems (CISS), Mar S. Sridharan and S. Vishwanath, On the capacity of a class of mimo cognitive radios, in Information Theory Workshop, ITW 07. IEEE, Sept. Y. Liang, A. Somekh-Baruch, H. V. Poor, S. Shamai, and S. Verdú, Capacity of cognitive interference channels with and without secrecy, IEEE Trans. on Inf. Theory, vol. 55, no. 2, pp , Feb Cognitive Z interference channel N. Liu, I. Maric, A. Goldsmith, and S. Shamai, The capacity region of the cognitive z-interference channel with one noiseless component, [Online]. Available: Degrees of Freedom of Cognitive Channels Chiachi Huang, Syed A. Jafar, ``Degrees of Freedom of the MIMO Interference Channel with Cooperation and Cognition, IEEE Transactions on Information Theory, Vol. 55, No. 9, Sep. 2009, Pages: Wyner-type cognitive networks A. Lapidoth, N. Levy, S. Shamai (Shitz), and M. A. Wigger, ``A Cognitive Network with Clustered Decoding, in Proc. ISIT 2009, Seoul, Korea, June 28-July 3, A. Lapidoth, S. Shamai (Shitz), and M. A. Wigger, ``On Cognitive Interference Networks, in Proc. ITW 2007, Lake Tahoe, USA, Sep. 2-6, A. Lapidoth, S. Shamai (Shitz), and M. A. Wigger, ``A Linear Interference Network with Local Side-Information, in Proc. ISIT 2007, Nice, France, June 24-29, Interference N. Devroye, P. Mitran, and V. Tarokh, channel Cognitive multiple access with networks, cognitive in Proc. IEEE Int. Symp. Inf. relay Theory, 2005, pp O. Sahin and E. Erkip, Achievable rates for the gaussian interference relay channel, in Proc. of IEEE Globecom, Washington D.C., Nov , On achievable rates for interference relay channel with interference cancellation, in Proc. of Annual Asilomar Conference of Signals, Systems and Computers, Pacific Grove, Nov J. Jiang, I. Maric, A. Goldsmith, and S. Cui, Achievable rate regions for broadcast channels with cognitive radios, Proc. of IEEE Information Theory Workshop (ITW), Oct S. Sridharan, S. Vishwanath, S. Jafar, and S. Shamai, On the capacity of cognitive relay assisted gaussian interference channel, in Proc. IEEE Int. Symp. Information Theory, Toronto, Canada, 2008, pp E. Telatar and D. Tse, Bounds on the capacity region of a class of interference channels, Proc. IEEE Int. Symp. Inf. Theory, 2007.

7 Outer bound W. Wu, S. Vishwanath, and A. Arapostathis, Capacity of a class of cognitive radio channels: Interference channels with degraded message sets, Information Theory, IEEE Transactions on, vol. 53, no. 11, pp , Nov union over all distributions )

8 Outer bound simplifications Strong interference Weak interference >'2;2$#5),&8$(

9 Capacity in strong interference I. Maric, R. D. Yates, and G. Kramer, Capacity of Interference Channels With Partial Transmitter Cooperation, IEEE Trans. Inf. Theory, vol. 53, no. 10, pp , Oct I(Y 2 ; X 1,X 2 ) I(Y 1 ; X 1,X 2 ) 9 &"'"%$()*

10 Capacity in very weak interference vol. 54, no. 10, pp , Oct A. Jovicic and P. Viswanath, Cognitive radio: An information-theoretic perspective, Proc. IEEE Int. Symp. Inf. Theory, pp , July G. W. Kramer, Wu, S. Topics Vishwanath, in Multi-User and A. Information Arapostathis, Theory, Capacity ser. Foundations of a class of and cognitive Trends in radio Communications channels: Interference and Information channels Theory. with Vol. degraded 4: No message 45, pp sets, Information Theory, IEEE Transactions on, vol. 53, no. 11, pp , Nov ()*)'&+,-

11 Contributions Tx 1 new inner bound (largest region) new outer bound (not tightest, but computable) capacity for deterministic channels (also semi-deterministic) 1.8 bit gap result for Gaussian channels (preliminary simulations show smaller gap)

12 Achievable scheme Tx 1 rate-splitting Gel fand-pinkser binning superposition coding c = common, p = private, a = alone, b = broadcast

13 Tx 1 c = common, p = private, a = alone, b = broadcast Superposition

14 Tx 1 c = common, p = private, a = alone, b = broadcast Binning

15 Tx 1 c = common, p = private, a = alone, b = broadcast R 1c I(U 1c ; X 2 U 2c ) R 1c + R 1pb I(U 1pb,U 1c ; X 2 U 2c ) R 1c + R 1pb + R 2pb I(U 1pb,U 1c ; X 2 U 2c )+I(U 2pb ; U 1pb U 1c,U 2c,X 2 ) R 2c + R 2pa +(R 1c + R 1c)+(R 2pb + R 2pb) I(Y 2 ; U 2pb,U 1c,X 2,U 2c )+I(U 1c ; X 2 U 2c ) R 2pa +(R 1c + R 1c)+(R 2pb + R 2pb) I(Y 2 ; U 2pb,U 1c,X 2 U 2c )+I(U 1c ; X 2 U 2c ) R 2pa +(R 2pb + R 2pb) I(Y 2 ; U 2pb,X 2 U 1c,U 2c )+I(U 1c ; X 2 U 2c ) (R 1c + R 1c)+(R 2pb + R 2pb) I(Y 2 ; U 2pb,U 1c X 2,U 2c )+I(U 1c ; X 2 U 2c ) (R 2pb + R 2pb) I(Y 2 ; U 2pb U 1c,X 2,U 2c ) R 2c +(R 1c + R 1c)+(R 1pb + R 1pb) I(Y 1 ; U 1pb,U 1c,U 2c ), for some input distribution (R 1c + R 1c)+(R 1pb + R 1pb) I(Y 1 ; U 1pb,U 1c U 2c ), (R 1pb + R 1pb) I(Y 1 ; U 1pb U 1c,U 2c ), p Y1,Y 2,X 1,X 2,U 1c,U 2c,U 1pb,U 2pb = p U1c,U 2c,U 1pb,U 2pb p X1,X 2 U 1c,U 2c,U 1pb,U 2pb p Y1,Y 2 X 1,X 2. Proof: The meaning of the random variables (RV) in Theorem I.1 is as follows. Both transmitters perform

16 Tx 1 c = common, p = private, a = alone, b = broadcast Very weak interference - capacity 8 9 vol. 54, no. 10, pp , Oct A. Jovicic and P. Viswanath, Cognitive radio: An information-theoretic perspective, Proc. IEEE Int. Symp. Inf. Theory, pp , July W. G. Kramer, Wu, S. Topics Vishwanath, in Multi-User and A. Information Arapostathis, Theory, Capacity ser. Foundations of a class of andcognitive Trends inradio Communications channels: Interference and Information channels Theory. with degraded Vol. 4: Nomessage 45, pp sets, Information Theory, IEEE Transactions on, vol. 53, no. 11, pp , Nov

17 Tx 1 c = common, p = private, a = alone, b = broadcast!"#$%&'()**+,-.*/)*0121 Strong interference - capacity 8 I(Y 2 ; X 1,X 2 ) I(Y 1 ; X 1,X 2 ) 9 I. Maric, R. D. Yates, and G. Kramer, Capacity of Interference Channels With Partial Transmitter Cooperation, IEEE Trans. Inf. Theory, vol. 53, no. 10, pp , Oct

18 Tx 1 c = common, p = private, a = alone, b = broadcast Analytically shown to be largest known region R 1c I(U 1c ; X 2 U 2c ) R 1c + R 1pb I(U 1pb,U 1c ; X 2 U 2c ) R 1c + R 1pb + R 2pb I(U 1pb,U 1c ; X 2 U 2c )+I(U 2pb ; U 1pb U 1c,U 2c,X 2 ) R 2c + R 2pa +(R 1c + R 1c)+(R 2pb + R 2pb) I(Y 2 ; U 2pb,U 1c,X 2,U 2c )+I(U 1c ; X 2 U 2c ) R 2pa +(R 1c + R 1c)+(R 2pb + R 2pb) I(Y 2 ; U 2pb,U 1c,X 2 U 2c )+I(U 1c ; X 2 U 2c ) R 2pa +(R 2pb + R 2pb) I(Y 2 ; U 2pb,X 2 U 1c,U 2c )+I(U 1c ; X 2 U 2c ) (R 1c + R 1c)+(R 2pb + R 2pb) I(Y 2 ; U 2pb,U 1c X 2,U 2c )+I(U 1c ; X 2 U 2c ) (R 2pb + R 2pb) I(Y 2 ; U 2pb U 1c,X 2,U 2c ) R 2c +(R 1c + R 1c)+(R 1pb + R 1pb) I(Y 1 ; U 1pb,U 1c,U 2c ), for some input distribution (R 1c + R 1c)+(R 1pb + R 1pb) I(Y 1 ; U 1pb,U 1c U 2c ), (R 1pb + R 1pb) I(Y 1 ; U 1pb U 1c,U 2c ), p Y1,Y 2,X 1,X 2,U 1c,U 2c,U 1pb,U 2pb = p U1c,U 2c,U 1pb,U 2pb p X1,X 2 U 1c,U 2c,U 1pb,U 2pb p Y1,Y 2 X 1,X 2. Proof: The meaning of the random variables (RV) in Theorem I.1 is as follows. Both transmitters perform

19 Contributions Tx 1 new inner bound (largest region) new outer bound (not tightest, but computable) capacity for deterministic channels (also semi-deterministic and linear high-snr)) 1.8 bit gap result for Gaussian channels (preliminary simulations show smaller gap)

20 New outer bound Tx 1 )3:7;)";#" Fig. 11. interfering links. Ideas about what the teaser may correspond to in Gaussian noise may be nice to put in. [3] Sato s worst joint same marginal idea REFERENCES [1] A. E.-G. M. Costa, The capacity region of the discrete memoryless interference channel with strong interference. IEEE Transactions on Information Theory, vol. 33, no. 5, pp , [2] H. Sato, An outer bound to the capacity region of broadcast channels, IEEE Trans. Inf. Theory, vol. IT-24, pp , May [3] L. Ghabeli and M. R. Aref, A new achievable rate and the capacity of a class of semi-deterministic relay networks, in Proc. IEEE Int. Symp. Inf. Theory, June 2007, pp

21 Contributions Tx 1 new inner bound (largest region) new outer bound (not tightest, but computable) capacity for deterministic channels (also semi-deterministic) 1.8 bit gap result for Gaussian channels (preliminary simulations show smaller gap)

22 Deterministic channels Tx 1 Outer bound becomes Achievable for certain channels including the deterministic (semi-deterministic, linear high SNR deterministic) channels

23 Deterministic channels: capacity Tx 1 B A

24 Deterministic channels: capacity B A Point A Point B

25 Contributions Tx 1 new inner bound (largest region) new outer bound (not tightest, but computable) capacity for deterministic channels (also semi-deterministic and linear high-snr)) 1.8 bit gap result for Gaussian channels (preliminary simulations show smaller gap)

26 High-SNR linear deterministic models A. Avestimehr, S. Diggavi, and D. Tse, A deterministic approach to wireless relay networks, in Proc. Allerton Conf. Commun., Control and Comp., Monticello, Sept , A deterministic model for wireless relay networks and its capacity, in Proc. IEEE Inf. Theory Workshop, Bergen, July 2007, pp ] G. Bresler and D. Tse, The two-user gaussian interference channel: A deterministic view, European Transactions in Telecommunications, vol. 19, pp , Apr S. Rini, D. Tuninetti, and N. Devroye, The capacity region of the gaussian cognitive radio channel at high SNR, in Proc. IEEE Inf. Theory Workshop, Taormina, Oct Constant gap results using deterministic intuition R. Etkin, D. Tse, and H. Wang, Gaussian interference channel capacity to within one bit, IEEE Trans. Inf. Theory, vol. 54, no. 12, pp , Dec G. Bresler, A. Parekh, and D. Tse, The approximate capacity of the many-to-one and one-tomany gaussian interference channels, [Online]. Available: S. Rini, D. Tuninetti, and N. Devroye, The capacity region of gaussian cognitive radio channels to within 1.87 bits, Proc. IEEE ITW Cairo, Egypt, 2010, devroye/conferences.html. ] A. Avestimehr, A. Sezgin, and D. Tse, Capacity region of the deterministic multi-pair bidirectional relay network, in Proc. IEEE Inf. Theory Workshop, Volos, June ], Approximate capacity of the two-way relay channel: a deterministic approach, in Proc. Allerton Conf. Commun., Control and Comp., Monticello, IL, Sept. 2008, pp M. Anand and P. Kumar, On approximating gaussian relay networks by deterministic networks, [Online]. Available: V. Prabhakaran and P. Viswanath, Interference channels with source cooperation, [Online]. Available:

27 High-SNR linear deterministic cognitive interference channel REFERENCES [1] S. Rini, D. Tuninetti, and N. Devroye, The capacity region of deterministic cognitive radio channels, Proc. IEEE ITW Taormina, Italy, vol. Oct., [2] A. E.-G. M. Costa, The capacity region of the discrete memoryless interference channel with strong interference. IEEE Transactions on Information Theory, vol. 33, no. 5, pp , [3] H. Sato, An outer bound to the capacity region of broadcast channels, IEEE Trans. Inf. Theory, vol. IT-24, pp , May [4] L. Ghabeli and M. R. Aref, A new achievable rate and the capacity of a class of semi-deterministic relay networks, in Proc. IEEE Int. Symp. Inf. Theory, June 2007, pp Tx 1

28 High-SNR linear deterministic cognitive interference channel REFERENCES [1] S. Rini, D. Tuninetti, and N. Devroye, The capacity region of deterministic cognitive radio channels, Proc. IEEE ITW Taormina, Italy, vol. Oct., [2] A. E.-G. M. Costa, The capacity region of the discrete memoryless interference channel with strong interference. IEEE Transactions on Information Theory, vol. 33, no. 5, pp , [3] H. Sato, An outer bound to the capacity region of broadcast channels, IEEE Trans. Inf. Theory, vol. IT-24, pp , May [4] L. Ghabeli and M. R. Aref, A new achievable rate and the capacity of a class of semi-deterministic relay networks, in Proc. IEEE Int. Symp. Inf. Theory, June 2007, pp Tx 1 Tx 1 Tx 1 D-IFC D-CIFC MIMO-BC!"#$%&'(%)*+*,-"."/+"0%0$1..*2/

29 Contributions Tx 1 new inner bound (largest region) new outer bound (not tightest, but computable) capacity for deterministic channels (also semi-deterministic and linear high-snr)) 1.8 bit gap result for Gaussian channels (preliminary simulations show smaller gap)

30 High-SNR deterministic C-IFC Tx 1 Gaussian C-IFC b a 3!4)**+,-.*5)*0121!"#$%&'()**+,-.*/)*0121

31 New outer bound b a 3!4)**+,-.*5)*0121!"#$%&'()**+,-.*/)*0121 )3:7;)";#" Fig. 11. interfering links. Ideas about what the teaser may correspond to in Gaussian noise may be nice to put in. [3] Sato s worst joint same marginal idea REFERENCES [1] A. E.-G. M. Costa, The capacity region of the discrete memoryless interference channel with strong interference. IEEE Transactions on Information Theory, vol. 33, no. 5, pp , [2] H. Sato, An outer bound to the capacity region of broadcast channels, IEEE Trans. Inf. Theory, vol. IT-24, pp , May [3] L. Ghabeli and M. R. Aref, A new achievable rate and the capacity of a class of semi-deterministic relay networks, in Proc. IEEE Int. Symp. Inf. Theory, June 2007, pp

32 Gaussian outer bound b a Theorem III.1. The capacity region of a G-CIFC is within the convex-hull of R log ( 1 + (1 ρ 2 ) )P 1 (2a) R 2 1 ( 2 log 1+ b 2 P 1 + P 2 +2ρ ) b 2 P 1 P 2 (2b) R 1 + R 2 1 ( 2 log 1+ b 2 P 1 + P 2 +2ρ ) b 2 P 1 P log ( 1 + (1 ρ 2 ) max{1, b 2 }P (1 ρ 2 ) b 2 P 1 for all ρ [0, 1]. 3!4)**+,-.*5)*0121 ) (2c)!"#$%&'()**+,-.*/)*0121 unifies bounds of [Maric et al.] and [Wu et al.] by proper choice of S. Rini, D. Tuninetti, and N. Devroye, The capacity region of gaussian cognitive radio channels to within 1.87 bits, Proc. IEEE ITW Cairo, Egypt, vol

33 Known Gaussian results b a 3!4)**+,-.*5)*0121 (!"#$%&'()**+,-.*/)*0121 ( ) α a α 2 + b 2 1+2ραb + ρ 2 ρ, α P 1 /P 2, for every ρ 1. '(.*& $+0()2()(+-( 3()1&%0),+4& $+0()2()(+-( 5 6 We prove a finite gap

34 Proving a finite gap 1 b a 3!4)**+,-.*5)*0121!"#$%&'()**+,-.*/)*0121 ) 56+! 7#%,#$.8!"#$%&'(")* +#%,-./#&0-)$&,11%(2-3,#-()&(4& ("#$%&'(")* +(3$ 7#%,#$.8 9(")*&#/-7&3,2-3"3& *-7#,):$&!"#$%&'()*+,)-.)/010

35 Proving a finite gap 1 b a 3!4)**+,-.*5)*0121!"#$%&'()**+,-.*/)*0121!"'&$9:2+#;)<$"+'%+'+$7+)!"'&$9:2+#;)!49$#=!"#$%&'()*+,)-.)/010 (with respect to the primary receiver 2)

36 Proving a finite gap b a 3!4)**+,-.*5)*0121!"#$%&'()**+,-.*/)*0121 ) 376+'6&38"8&$4252,'&#(2#3"4256!"#$%&'()*+,)-.)/010 9:;4256

37 Proving a finite gap ) b a 376+'6&38"8&$4252 3!4)**+,-.*5)*0121!"#$%&'()**+,-.*/)*0121,'&#(2#3"4256!"#$%&'()*+,)-.)/010 9:;4256 Compound MAC-like in strong interference!!"#$%&'()**+,-.*/)*0121

38 Proving a finite gap ) b a 376+'6&38"8&$4252 3!4)**+,-.*5)*0121!"#$%&'()**+,-.*/)*0121,'&#(2#3"4256!"#$%&'()*+,)-.)/010 9:;4256 Broadcasting strategy at the cognitive Tx!

39 Proving a finite gap ) b a 376+'6&38"8&$4252 3!4)**+,-.*5)*0121!"#$%&'()**+,-.*/)*0121,'&#(2#3"4256!"#$%&'()*+,)-.)/010 9:;4256 Binning strategy at the cognitive Tx! Play with Costa s DPC coefficient!

40 Proving a finite gap 2 b a 3!4)**+,-.*5)*0121!"#$%&'()**+,-.*/)* bits Unified strategy

41 Numerical simulations are promising b a 3!4)**+,-.*5)*0121!"#$%&'()**+,-.*/)*0121 )

42 Contributions Tx 1 new inner bound (largest region) new outer bound (not tightest, but computable) capacity for deterministic channels (also semi-deterministic) 1.8 bit gap result for Gaussian channels (preliminary simulations show smaller gap) Thank you Stefano Rini, Ph.D. candidate, srini2@uic.edu Daniela Tuninetti, danielat@uic.edu Natasha Devroye, devroye@uic.edu