Cooperative Communication Fundamentals & Coding Techniques

Size: px

Start display at page:

Download "Cooperative Communication Fundamentals & Coding Techniques"

Chrystal West
5 years ago
Views:

1 3 th ICACT Tutorial Cooperative commuicatio fudametals & codig techiques Cooperative Commuicatio Fudametals & Codig Techiques 0..4 Electroics ad Telecommuicatio Research Istitute Kiug Jug

2 3 th ICACT Tutorial Cooperative commuicatio fudametals & codig techiques Coverage. Preparatory Overview of Iformatio Theory Basics Iformatio theory basics & chael capacity Network iformatio theory basics Cooperative commuicatio examples - Simulcast trasmissio - Relay trasmissio ad iterative diversity Break. Codig Techiques for Cooperative Commuicatio Pricipal desig tools Cooperative codig schemes i wireless cooperative chaels

3 Sectio. Preparatory Overview Sectio Preparatory Overview of Iformatio Theory Basics 3

4 Sectio. Preparatory Overview Itroductio What is cooperative commuicatio? Classically, it refers to the relay chael We cosider it i a broader aspect as multi-termial commuicatios: The termials joitly use the medium as shared resource istead of oe that is divided orthogoally amog pairs of termials. 4

5 Sectio. Preparatory Overview Itroductio Motivatio Wireless etworks icreasigly take places importat i moder commuicatios. Typical wireless chael usage: Avoidig iterferece amog users by usig orthogoally divided chaels. Capacity approachig process Iformatio theory based resource sharig amog multiple termials rather tha usig orthogoally divided chaels. 5

6 Sectio. Preparatory Overview Itroductio Coverage of Cooperative Commuicatio Classically, it refers to the relay chael We cosider it i a broader aspect as multi-termial commuicatios: The termials joitly use the medium as shared resource istead of oe that is divided orthogoally amog pairs of termials. 6

7 Sectio. Preparatory Overview Itroductio A example: T.M. Cover s Broadcast Chael, 97 7

8 Sectio. Preparatory Overview Itroductio Why Now? Iformatio theoretical cosideratio o cooperatio has bee started sice the early 970s. It did NOT attract sigificat iterests util 003 ad beyod. 8

9 Sectio. Preparatory Overview Itroductio Why Now? Importace of mobile commuicatio - Fadig chael Importace of etworked commuicatio - Multiple commuicatios Ability to implemetatio - Sigal processig capability - Moder error-correctio codes 9

10 Sectio. Preparatory Overview Iformatio theory basics & chael capacity Review: Iformatio Theory Basics Etropy - Ucertaity - Average amout of iformatio per source output (* You became a father!! ) H pxlog px E x p log p -> Fuctio of the distributio * From Thomas Cover et al., Elemets of Iformatio Theory 0

11 Sectio. Preparatory Overview Iformatio theory basics & chael capacity Review: Iformatio Theory Basics Etropy - A measure of ucertaity of a radom variable. - Fuctio of distributio of a radom variable, which depeds oly o the probabilities. - Average amout of iformatio per source output. -> Chael capacity - Average legth of the shortest descriptio of the radom variable -> Expected descriptio legth must be greater tha or equal to the etropy. -> Data compressio

12 Sectio. Preparatory Overview Iformatio theory basics & chael capacity Review: Iformatio Theory Basics By the defiitio of the etropy Joit Etropy H, Y px, ylog px, y E p x y log Coditioal Etropy H p, Y Y px, ylog px y E p x y log p Y

13 Sectio. Preparatory Overview Iformatio theory basics & chael capacity Review: Iformatio Theory Basics Mutual Iformatio A measure of the amout of iformatio that oe radom variable cotais about aother radom variable. The, I ; Y px, y x E y p x, y log p p px, y pxpy, Y py log ; Y H H Y I -> The reductio i the ucertaity of due to the kowledge of Y. Chael Capacity C max p x I ; Y 3

14 Sectio. Preparatory Overview Iformatio theory basics & chael capacity Review: Iformatio Theory Basics The Asymptotic Equipartitio Property (AEP) - The aalog of the law of large umbers. - The law of large umbers states that for i.i.d. radom variables, i i E, for large - The AEP states that; log So, p p,,..., p,,..., : H,,..., H, where,,..., are i. i. d. Probabilit y of observig the sequece,,..., - This arises the typical set i all sequeces where the sample etropy is close to true etropy. 4

15 Sectio. Preparatory Overview Iformatio theory basics & chael capacity Review: Iformatio Theory Basics Typical Set, A - Typical sequeces determie the average behavior of a large sample with high probability. - The umber of elemets i the typical set is early H where A H is a arbitrary small umber accordig to a appropriate choice of. : elemets No - typical set Typical H sets, A : elemets 5

16 Sectio. Preparatory Overview Iformatio theory basics & chael capacity Review: Iformatio Theory Basics Theorem 3.. (T. M. Cover, p54) 0 - Let be i. i. d. ~ p x. Let. The there exists a code which x maps sequeces of legth ito biary strigs such that the mappig is oe-to-oe (ad therefore ivertible) ad E l For sufficietly large, x l H : deote a sequece x, x,..., x x :legth of th codeword correspodig to x - Thus we ca represet sequeces usig bits o the average. H 6

17 Sectio. Preparatory Overview Iformatio theory basics & chael capacity Review: Chael Capacity Iformatio Chael Capacity C max p x I ; Y Operatioal Chael Capacity - Highest rate i bits per chael use at which iformatio ca be set with arbitrarily low probability of error. Shao s secod theorem establishes Iform. Chael Capacity = Oper. Chael Capacity 7

18 Sectio. Preparatory Overview Iformatio theory basics & chael capacity Shao s secod theorem - Operatioal meaig to the defiitio of capacity as the umber of bits we ca trasmit reliably over the chael. Basic Idea - For each (typical) iput -sequeces, there are approximately H Y Review: Chael Capacity possible Y sequeces, all of them equally likely. W Y Wˆ - The total umber of possible (typical) Y sequeces is. - This set has to be divided ito sets of size correspodig to the differet iput sequeces. H Y H Y 8

19 Sectio. Preparatory Overview Iformatio theory basics & chael capacity Basic Idea (cotiued) - The total umber of disjoit sets is H Y H Y I ; Y. - Hece we ca sed at most I ; Y distiguishable sequeces of legth. Theorem 8.7. (T. M. Cover, p98) The chael codig theorem: All rates below capacity achievable. Specifically, for every rate sequece of Review: Chael Capacity, there exists a are R, codes with maximum probability of error 0 Coversely, ay sequece of codes with must have R C max p x R C C R, 0 I ; Y 9

20 Sectio. Preparatory Overview Iformatio theory basics & chael capacity Gaussia Chael Review: Chael Capacity - The most commo limitatio o the iput is power costrait. - Iput ad output Y radom variables are cotiuous. Y i i Z i i x i i P, Z ~ N 0, - Differetial etropy h of a cotiuous radom variable; h f xlog f xdx, f x ~ pdf for S - For a ormal distributio, (T. M. Cover, p5) ~ x e h log e bits 0

21 Sectio. Preparatory Overview Iformatio theory basics & chael capacity Review: Chael Capacity Iformatio Capacity i Gaussia Chael I C x : E P ; Y hy hy hy h Z hy h( Z ) hy hz,, Z ~ idepede t where, h With power costrait, p max I ; Y Z log en, EY E Z E EZ P N I E P ; Y hy hz log e log P N P N. i ~ log en P, P Z i ~ 0, N Y i

22 Sectio. Preparatory Overview Iformatio theory basics & chael capacity Review: Chael Capacity Iformatio Capacity i Gaussia Chael C bits per trasm issio max ; log : I Y p x E P N P A rate R is said to be achievable for a Gaussia chael with a power costrait P if there exists a sequece of R, codes with code words satisfyig the power costrait such that the maximal probability of error teds to zero. R C

23 Sectio. Preparatory Overview Iformatio theory basics & chael capacity Review: Chael Capacity Bad-Limited Gaussia Chael - A commo model for commuicatio over a radio etwork is a bad-limited with white oise. Nyquist-Shao samplig theorem - Samplig a bad-limited sigal at a samplig rate is sufficiet to recostruct the sigal from the samples. W 3

24 Sectio. Preparatory Overview Iformatio theory basics & chael capacity Review: Chael Capacity So, for a Bad-Limited Gaussia Chael, N 0 W 0,T if Nose PSD ~, Badwidth, Time iterval C log log P N P W Sice there are bits W N per trasmissio 0 log P N W 0 bits samples each secod, per samples. C W log P N W 0 bits per secod. 4

25 Badwidth efficiecy, Rb/W bit/sec/hz Sectio. Preparatory Overview Iformatio theory basics & chael capacity Review: Chael Capacity Shao limit The limitig value of Eb/No below which there ca be o error-free commuicatio at ay iformatio rate Badwidth Efficiecy A measure of how much data ca be commuicated i a specified badwidth withi a give time. The Badwidth Efficiecy Diagram R W Shao Limit Capacity boudary R=C Bit to oise ratio, Eb/No db 5

26 Sectio. Preparatory Overview Network iformatio theory basics Multiple Access Chael (MAC) Two or more seders ad a commo receiver. Defiitio: A rate pair R, R is said to be achievable for the multiple access chael if there exists a sequece of codes with 0. P e R R,, 6

27 Sectio. Preparatory Overview Network iformatio theory basics 7 Multiple Access Chael (MAC) Capacity regio The closure of the covex hull of the set of poits satisfyig; R, R ;, ; ; Y I R R Y I R Y I R R R ; Y I ; Y I Y I ; Y I ; A D C B

28 Sectio. Preparatory Overview Network iformatio theory basics Multiple Access Chael (MAC) Poit A Maximum rate achievable from seder whe seder is ot sedig ay iformatio. max R Poit B max I ; Y p x p x I Y ; R D C - Maximum rate seder ca sed as log as seder I ; Y B seds at this maximum rate. - is cosidered as oise for the chael Y I ; Y I A Y ; R 8

29 Sectio. Preparatory Overview Network iformatio theory basics 9 Multiple Access Chael (MAC) Gaussia Multiple Access chael - For some iput distributio, R R N P C N P C N P P C N P P C x f x f ad P E P E - Defie chael capacity fuctio with sigal to oise ratio x, log x x C The,.,, N P P C R R N P C R N P C R

30 Sectio. Preparatory Overview Network iformatio theory basics 30 Suppose there are two sources What if the -source ad the Y-source must be separately? Ecodig of Correlated Sources Y H R R Y H R Y H R,,,

31 Sectio. Preparatory Overview Network iformatio theory basics Slepia-Wolf Ecodig Radom biig procedure. Very similar to hash fuctios. With high probability, differet source sequeces have differet idices, ad we ca recover the source sequece from the idex. Rate regio for Slepia-Wolf ecodig. 3

32 Sectio. Preparatory Overview Network iformatio theory basics Broadcast Chael Oe seder ad two or more receivers. TV statio Superpositio of iformatio We may wish to arrage the iformatio i such a way that the better receivers receive extra iformatio, which produces a better picture or soud. 3

33 Sectio. Preparatory Overview Network iformatio theory basics Broadcast Diversity Coceptual example 33

34 Sectio. Preparatory Overview Network iformatio theory basics Broadcast Diversity 34

35 Sectio. Preparatory Overview Network iformatio theory basics Relay Chael Oe seder ad oe receiver with a umber of itermediate odes. The relay chael combies a broadcast chael ad a multiple access chael. C sup p x, x mi I, ; Y, I ; Y, Y 35

36 Sectio. Preparatory Overview Cooperative commuicatio examples Example I: Relay Trasmissio Decode-ad-forward, Laema, 00 * Diversity chael is created oly whe the relay decodes successfully. 36

37 Sectio. Preparatory Overview Cooperative commuicatio examples Example I: Relay Trasmissio Amplify-ad-forward, Laema, 00 * The relay also amplifies its ow receiver oise. 37

38 Sectio. Preparatory Overview Cooperative commuicatio examples Example I: Relay Trasmissio Coded cooperatio, T. E. Huter, 00 * Rate-Compatible Puctured Covolutioal code (RCPC) based 38

39 Sectio. Preparatory Overview Cooperative commuicatio examples Example I: Relay Trasmissio Cooperatio usig turbo codes, Zhao ad Valeti, 003 Decode ad permute * Two separate Recursive Systematic Covolutioal (RSC) ecoders costitutes turbo ecoder followed by iterative decodig betwee the relay ad the destiatio 39

40 Sectio. Preparatory Overview Cooperative commuicatio examples Example I: Iterative Diversity Collaborative decodig, Aru ad J. M. Shea, System model for collaborative decodig - Priciple of collaborative decodig with two odes 40

41 Sectio. Preparatory Overview Cooperative commuicatio examples Example I: Iterative Diversity 3 iteratios, 5% LRB exchage, 900 packet size Performace of two collaborative decodig schemes i which receivers request iformatio for a set of least-reliable bits. 4

42 Sectio. Preparatory Overview Cooperative commuicatio examples Example II: Simulcast Trasmissio Simulcast by usig No-Uiform QPSK UEP sigalig, K. Jug & J. Shea, 005 b : Basic message b : Additioal message Typical required bit error probability - for voice: for data: 0-4 4

43 Sectio. Preparatory Overview Cooperative commuicatio examples Example II: Simulcast Trasmissio Example of trasmissio rage calculatio - Sigalig: 4-PSK - Degradatio: 0.3dB (θ=5 o ) - Disparity:.4dB (P B =P A ) - Origial trasmissio rage by BPSK: 00m - Propagatio costat, : 4 43

44 Sectio. Preparatory Overview Cooperative commuicatio examples Example II: Simulcast Trasmissio Simulcast by usig No-Uiform QPSK UEP sigalig G S S ete ete 0 Simulatio results of ETE throughput at =4, Poisso distributio of H(θ) 44

Entropies & Information Theory

Entropies & Information Theory Etropies & Iformatio Theory LECTURE I Nilajaa Datta Uiversity of Cambridge,U.K. For more details: see lecture otes (Lecture 1- Lecture 5) o http://www.qi.damtp.cam.ac.uk/ode/223 Quatum Iformatio Theory