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									SIMPLY COOPERATIVE

    Anthony Ephremides

   Pompeu Fabra University

        April 29, 2010

     Barcelona, Catalunia
                             1
THE “COAT OF ARMS”




S: source       D: destination




                                 2
THE “COAT OF ARMS”

            R: relay




S: source              D: destination




                                        3
     THE “COAT OF ARMS”
                 l2
                      R: relay
                         and source




l1

     S: source                        D: destination




                                                       4
     THE “COAT OF ARMS”
                    l2
                         R: relay
                            and source




l1

     S: source                           D: destination
                 “ether” medium




                                                          5
THE “HISTORY”




                6
                THE “HISTORY”
− “RELAY” CHANNEL (Van der Meulen ‟60‟s)
                   R
                                  Key differences
                              No “source” traffic from R

                              No “ether”
reservoir                     Classical information-theoretic
            S             D   quest for capacity – backlogged S




                                                                  7
                   THE “HISTORY”
− “RELAY” CHANNEL (Van der Meulen ‟60‟s)
                           R
                                           Key differences
                                       No “source” traffic from R

                                       No “ether”
reservoir                              Classical information-theoretic
              S                    D   quest for capacity – backlogged S
− “REVISED” RELAY CHANNEL
                                          ( − Laneman/Tse/Wornell
         (wireless)                        − Sendonaris /Erkip/Aazhang
                                           − Kramer/ Gastpar/Gupta
                                           − Kramer/Maric/Yates
                                             …………………… )
            Basic idea: Cooperative Diversity
                        (variety of schemes)
             Objective: Again, Capacity (backlogged S)

                                                                           8
A “WIRELESS” NETWORK PERSPECTIVE




                                   9
 A “WIRELESS” NETWORK PERSPECTIVE
• “PACKETS”         THROUGHPUT




                                    10
 A “WIRELESS” NETWORK PERSPECTIVE
• “PACKETS”          THROUGHPUT
• “BURSTY TRAFFIC”   DELAY




                                    11
 A “WIRELESS” NETWORK PERSPECTIVE
• “PACKETS”            THROUGHPUT
• “BURSTY TRAFFIC”      DELAY



          − STABLE THROUGHPUT




                                    12
 A “WIRELESS” NETWORK PERSPECTIVE
• “PACKETS”               THROUGHPUT
• “BURSTY TRAFFIC”        DELAY



          − STABLE THROUGHPUT
          − COGNITION
              (sensing)




                                       13
 A “WIRELESS” NETWORK PERSPECTIVE
• “PACKETS”               THROUGHPUT
• “BURSTY TRAFFIC”        DELAY



          − STABLE THROUGHPUT
          − COGNITION
              (sensing)


      Q: CAN’T WE STILL CO-OPERATE?


                                       14
DIGRESSION: THE VIRTUE OF THE SINGLE QUEUE
                                   or
                   (STATISTICAL MULTIPLEXING)

                                        SM
                   S1
                               D

                   S2




                         S                   D
  l1+ l2+…+ lM

                 “VIRTUAL” QUEUE

                                                 15
            THE “PRIMITIVE” IDEA
                                               (Sadek, Liu, Ephremides 2007)
     Source Terminals

l1               S1
                                                      • NO CONTENTION (e.g.
                                                        TDMA)
l2               S2                                   • PERFECT CHANNEL
                                                        SENSING
                              Relay R         D       • INSTANT ERROR-FREE
                                      hrd               “ACKs”
                        hir
li               Si                       Destination • SINR > b
                                 hid                  • FADING CHANNELS
                                                        (i.e. packet erasure
                                                        channels)
lM               SM

                                        | hab |2 P    
                              Pab  Pr              b
                                        N0            
                                                                               16
     COOPERATION METHOD 1
• Each terminal transmits HOL packet in its assigned slot (if
  empty, slot is free)
• If D receives successfully, it sends ACK (heard by both the
  relay and the user)
• If D does not succeed but R does: at first sensed empty slot
  R transmits to D the failed packet
• If neither D nor R succeed, packet gets retransmitted by the
  terminal in next frame
• Relay does not keep packets after the end of the frame
Remarks:
1. Relay has always a finite queue (M packets Max)   Idle slots are utilized!
2. Terminal queues “interact”


                                                                           17
      COOPERATION METHOD 2
• Each terminal transmits HOL packet in its assigned slot (if
  empty, slot is free)
• If D receives successfully, it sends ACK (heard by both the
  relay and the user)
• If D does not succeed but R does: at first sensed empty slot
  R transmits to D the failed packet
• If neither D nor R succeed, packet gets retransmitted by the
  terminal at next opportunity
• Relay keeps all packets it receives correctly
Remarks:
1. Relay has a possibly growing queue      Again: Idle slots are
2. Terminal queues do not interact              utilized!

                                                                 18
                     THE CRITERION
  STABLE THROUGHPUT:
   arrival rate                   service rate
            l                         m

                    Q(t): queue size at time t

             lim PrQ(t )  N  N  0
                                                        ~ “positive recurrence”
             t 



Loynes: If arrival process and service process are jointly stationary,
        the queue is stable iff l < m

                                       max stable throughput


                                                                               19
        THE CRITERION (cont.)
          Q1(t)                                              l2
                                                                         Set of λ ’s such that
 l1                                                                      Q1 and Q2 are stable
                                 service

 l2
          Q2(t)                                                              l1
Problem: When Q1(t) and Q2(t) “interact”, stationary “service rate”
         cannot be identified.
                    Q2             l2                   l2
                         m 2'     l1               l1               l1
                   l2
                                m1            m1                   m1

                   l2    m 2'                 l
                                   l1 l2 m2 l1 2 m2 l1                   m1 '≠ m1
                                m1         m1      m1
                                                                         m2 '≠ m2
                   l2    m2'         l1
                                          l2 m2    l
                                                l1 2 m2 l1
                                m 1'          m 1'                m 1'     Q1

Solution: STOCHASTIC DOMINANCE (Rao, Ephremides 1988)

                                                                                                 20
    BACK TO THE “PRIMITIVE” SYSTEM
            •   COOP METHOD 1
            •   COOP METHOD 2
    no      •   RANDOM ACCESS
cooperation •   TDMA
            •   SELECTIVE “DECODE-AND-FORWARD”
                                 ---NETWORK VIEW
                                       i.e.
                                 EVERY PACKET
                                 USES TWO SLOTS
                                      OR
                                 EVERY PACKET
                                 USES TWO “HALF-SLOTS”
                                 AS TWICE THE RATE




                                                         21
    BACK TO THE “PRIMITIVE” SYSTEM
            •   COOP METHOD 1
            •   COOP METHOD 2
    no      •   RANDOM ACCESS
cooperation •   TDMA
            •   SELECTIVE “DECODE-AND-FORWARD”
                                 ---NETWORK VIEW
                                       i.e.
                                 EVERY PACKET
                                 USES TWO SLOTS
                                      OR
                                 EVERY PACKET
                                 USES TWO “HALF-SLOTS”
                                 AS TWICE THE RATE


                                  attention
                                                         22
 RESULT FOR 2-USERS
     0.5


     0.45
                                                   TDMA
     0.4                                           COOP1
                                                   COOP2
                                                   DF
                                                   ALOHA
     0.35


     0.3
l2




     0.25


     0.2


     0.15


     0.1


     0.05


      0
       0    0.05   0.1   0.15   0.2   0.25   0.3     0.35   0.4   0.45   0.5
                                      l
                                       1



                           Comparison
                                                                               23
                                     1                                                                                     1
                                                                                                                                                                     TDMA
                                                                                                                                                                     COOP2
                                0.9                                                                                       0.9                                        DF
                                                                     TDMA=COOP1                                                                                      ALOHA
Aggregate Maximum Stable Throughpt



                                                                     COOP2
                                0.8                                  DF                                                   0.8
                                                                     ALOHA
                                0.7                                                                                       0.7




                                                                                        Aggregate Max Stable Throughput
                                0.6                                                                                       0.6


                                0.5                                                                                       0.5


                                0.4                                                                                       0.4


                                0.3                                                                                       0.3


                                0.2                                                                                       0.2


                                0.1                                                                                       0.1


                                     0                                                                                     0
                                      0      5     10    15     20       25   30   35                                       1      2   3    4    5     6     7   8    9        10

                                                 SNR Thresold (b) [dB]                                                                          R [b/s/Hz]

                                                                                                                               DF: Relay transmits at twice the rate and
                                          DF: Relay transmits at the same rate
                                                                                                                               utilizes one time slots. (Rate and SNR-
                                          and utilizes two time slots.
                                                                                                                               threshold are related through the
                                                                                                                               Gaussian mutual information formula.
                                                                                                                                                                          24
                                             DELAY
• Notoriously difficult for interacting queues
• Symmetric System: 2-users
                      5
                 10




                                     TDMA
                      4              COOP1
                 10
                                     COOP2
                                     DF
                                     ALOHA



                      3
 Average Delay




                 10




                      2
                 10




                      1
                 10




                      0
                 10
                          0   0.05     0.1    0.15   0.2   0.25   0.3   0.35   0.4
                                                     l1



                                                                                     25
              WHY?
VIRTUE OF THE SINGLE QUEUE
    l1   S1


   l2    S2
                     R     D




   lM    SM
                PARTIAL CONCENTRATION
                INTO SINGLE QUEUE
                IN METHOD 2



                                        26
S1
         BUT
S2
     R   D

SM




               27
S1
         BUT   S1


S2             S2
     R   D          D


SM             SM




                        28
       S1
                        BUT                        S1


       S2                                          S2
                    R     D                                             D


       SM                                          SM



            TANDEM IS BORN                piD
                                   piN
                                                 pND
   1        2             i                N                 D =(N+1)



ANY TERMINAL            Pij: Packet success probability from i to j
COULD PLAY THE               (increasing in i, decreasing in j, for i < j)
                                           or, simply
ROLE OF THE RELAY
                             (PiD increasing in i)

                                                                            29
HENCE, BACK TO THE „COAT OF ARMS”
                         l2
                                    2

                   p12                  p23

         l1
                   1          p13             3=D
NEW ISSUE:
     PRIORITY ORDER IN SERVING QUEUES AT “2”
   − AFFECTS DELAY (NOT THROUGHPUT)
ACCESS POLICY:
   −“ANY” CONFLICT-FREE “WORK-CONSERVING”
   −TDMA
      (MAXIMUM STABLE THROUGHPUT REGION: SAME)
    −RANDOM OR SCHEDULED ACCESS WITH MULTIPACKET
     RECEPTION
                        (B. Rong, A. Ephremides 2009)
                                                    30
 STABLE THROUGHPUT REGION

                                           • Both policies yield same
                                             stable throughput regions
                                             under cooperation
                                           • N users simultaneously
                                             increase stable
                                             throughput rates
                                           • lkmax , 1 ≤ k ≤ N-1
                                              lNmax
                                           • p1,2 increases 
                                             region increases


p1,3  0.3, p2,3  0.8, p1, 2  0.4,0.6,0.85

                                                                 31
       LESSON TAUGHT
− GAIN BY ALL USERS BECOMES
  MOTIVATION FOR COOPERATION




                               32
         LESSON TAUGHT
− GAIN BY ALL USERS BECOMES
  MOTIVATION FOR COOPERATION
          or
− IT IS IN THE INTEREST OF THE RICH TO
  HELP THE POOR




                                         33
          LESSON TAUGHT
− GAIN BY ALL USERS BECOMES
  MOTIVATION FOR COOPERATION
           or
− IT IS IN THE INTEREST OF THE RICH TO
  HELP THE POOR
Deeper and Far-reaching Interpretation:
     FOR BURSTY TRAFFIC IN SHARED CHANNELS,
     REDUCTION OF THE PRESENCE OF COMPETITION
     IS BENEFICIAL


                                           34
                             SEQUEL
•      STABLE THROUGHPUT REGION       S
    vs
       “BACKLOGGED” THROUGHPUT REGION T
                   S  T
        (FOR SCHEDULED ACCESS AND PRIORITY TO “NOT-TO-RELAY”)
       − COMMON PHENOMENON
• FOR RANDOM ACCESS (q1,q2) ON COLLISION
  CHANNEL, COOPERATION MAY HELP
                            COOP   S
                             S
                                      NC


                       p23  p12 (1  p13 )  p13 
        IF p13 
                        p12 1  p13      p23   
                                                   2


                                            (B. Rong, A. Ephremides ISIT 2009)

                                                                           35
 MULTI-PACKET RECEPTION CAPABILITY
                                    (B. Rong, A. Ephremides 2009)
• CRITERION:       SINR > g (simplest)
• NEW SET OF SUCCESS PROBABILITIES
• NO SIMULTANEOUS “TRANSMIT” AND “RECEIVE”
  BY R (initially)                            R
                      “Standard” channel
• PSR AS BEFORE
                      (J. Luo & A. Ephremides
• PRD > PRD/S     new 2006)
  PSD > PSD/R     new                    S                          D
   and of course PRD > PSD (Denote these probabilities by p )
 • R KNOWS WHETHER QS=0
COOPERATION POLICY:
      I. R MIXES OWN AND S‟s PACKETS
      II. IF QS=0, R TRANSMITS w.p. 1 (IF QR>0)
      III.IF QS>0, S TRANSMITS w.p. 1 AND R w.p. q (IF QR>0)
                                                                    36
                RESULT (MPR)
     A REGION OF VALUES OF THE PACKET
    SUCCESS PROBABILITIES, Λ ,SUCH THAT
①   IF    pΛ          COOP   S
                        S
                                 NC


       for suitable values of q
②   IF    pΛ        COOP   S for q=0
                        S
                                NC


       (i.e., scheduled transmission or “conventional”
       cooperation )



                                                         37
                                                               RESULT (cont.)
                                                                Resulting stability regions
                    0.7                                                                                              0.8
                                                                                     NC                                                                                             NC
                                                                                     CC                              0.7                                                            CC, C-OPP
                    0.6
                                                                                     C-OPP

                                                                                                                     0.6
                    0.5

                                                                                                                     0.5
l2 [packets/slot]




                                                                                                 l2 [packets/slot]
                    0.4
                                                                                                                     0.4
                    0.3
                                                                                                                     0.3

                    0.2
                                                                                                                     0.2

                    0.1                                                                                              0.1


                     0                                                                                                0
                          0    0.05   0.1   0.15     0.2     0.25      0.3   0.35   0.4   0.45                             0   0.05   0.1   0.15     0.2     0.25      0.3   0.35     0.4   0.45
                                                   l1 [packets/slot]                                                                               l1 [packets/slot]


                              If p  Λ , opportunistic                                                                         If p  Λ , the optimal
                              scheme results in improved                                                                       strategy is the conventional
                              stability region                                                                                 cognitive cooperation
                                                                                                                                                                                                   38
             --- AND MORE
• SIMILAR RESULTS FOR FULL TANDEM (MORE
  THAN TWO SOURCE TERMINALS)
• ENHANCEMENT WITH PHYSICAL-LAYER
  IMPROVEMENTS
  – COMBINE WITH DYNAMIC DECODE-AND-FORWARD
                (K. Azarian, H. El Gamal, P. Schniter 2005)
  – COMBINE WITH ADAPTIVE SUPERPOSITION CODING
                                           (T. Cover 1972)

     (B.Rong, I. Krikidis, A. Ephremides 2009)

                                                              39
                   RESULT




NC: no cooperation              CC: conventional cooperation
S-CC: conventional cooperation with superposition coding
NC-DDF: non-cognitive DDF       C-DDF: cognitive DDF
SC-DDF: cognitive DDF with superposition coding
                                                               40
     WHAT ABOUT NETWORK CODING?
                 QR1
            l2                 R: transmits random linear
                       R
                                  combinations of contents of
                 QR2              QR1 , QR2 (packet-by-packet)
l1
                                 −NO IMPROVEMENT
        S                  D

     --BUT: (i) IF THERE ARE MULTIPLE DESTINATIONS
                AND / OR
           (ii) CONTENTS OF BUFFERS ARE COMBINED IN
                THEIR ENTIRETY
                   − POSSIBLE IMPROVEMENT
                        (under investigation)

                                                                 41
         CONCLUSION
− RELAY-BASED COOPERATION AT THE
  PACKET LEVEL CAN BE BENEFICIAL
  FOR DIFFERENT REASONS (NOT
  DIVERSITY-RELATED)




                                   42
         CONCLUSION
− RELAY-BASED COOPERATION AT THE
  PACKET LEVEL CAN BE BENEFICIAL
  FOR DIFFERENT REASONS (NOT
  DIVERSITY-RELATED)
− TERMINALS CAN BE
      SIMPLY COOPERATIVE


                                   43

								
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