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Reverse Engineering MAC

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Reverse Engineering MAC. A. Tang (EE, Caltech, USA) Joint work with J.-W. Lee (EEE, ... J. Huang, M. Chiang, A. R. Calderbank (EE, Princeton University, USA) ... – PowerPoint PPT presentation

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Title: Reverse Engineering MAC


1
Reverse Engineering MAC
  • A. Tang (EE, Caltech, USA)
  • Joint work with J.-W. Lee (EEE, Yonsei
    University, Korea),
  • J. Huang, M. Chiang, A. R. Calderbank (EE,
    Princeton University, USA)
  • WiOpt 06 IEEE JSAC (to be published)

Presented by Kyung-Joon Park INDEX Group, CS
Department UIUC April 2, 2007
2
Reverse Engineering
  • Reverse engineering provides
  • Understanding properties of individual entity as
    well as overall system
  • Valuable guidance to improve system performance

3
Reverse Engineering
  • Reserve engineering in protocol layers
  • Layer 4 TCP/AQM Low03
  • Layer 3 BGP Griffin02
  • Layer 2 MAC (EB protocol based on persistence
    probabilities)
  • Utility based Reverse Engineering
  • What kind of utility functions do users have?
  • What kind of optimization problems does the
    protocol solve?

4
TCP/AQM Reverse Engineering
  • Can be modeled by Network Utility Maximization
    (NUM) problem
  • Utility of each user depends on its own data
    rate, which can be directly controlled by user
    itself
  • Feedback from network
  • Different TCP/AQM protocols result in different
    utility functions

5
MAC Reverse Engineering
  • Utility depends on its own transmission and other
    links transmissions through collisions
  • Cannot be controlled by link itself
  • No explicit feedback from network

Global optimization model??
Our approach non-cooperative game model
6
System Model
  • Persistence probabilistic model
  • Link l transmits with probability pl
  • If successful, pl plmax for next transmission
  • Otherwise, pl maxplmin,?lpl, where 0lt ?l lt 1
  • If ?l ½, exactly corresponds to BEB
  • Define
  • LIto(l) set of links whose transmissions cause
    interference to transmission of link l
  • LIfrom(l) set of links whose transmissions get
    interfered from transmission of link l

7
Persistence Probability Update
pl(t1) max plmin, plmax1Tl(t)1 1Cl(t)0
?l pl(t)
1Tl(t)11Cl(t)1 pl(t)1Tl(t)0
(1)
  • 1a indicator function of event a
  • Tl(t) event that link l transmits at time slot t
  • Cl(t) event that there is a collision to link
    ls transmission at time slot t

ProbTl(t)1p(t) pl(t) ProbCl(t)1p(t)1-
?n ? LtoI (l)(1-pn(t))
8
EB-MAC Game
  • Expected persistence probability
  • In (2), each link tries to maximize its utility
    Ul for given strategies of other links
  • Define EB-MAC game as
  • E set of players (links)
  • Al pl plmin ? pl ? plmax action set of
    link l
  • Ul utility function of link l

pl(t1) max plmin,plmax pl(t) ?n ?
LtoI(l)(1-pn(t)) ?l pl(t) pl(t) (1-
?n ? LtoI(l)(1-pn(t))) pl(t) (1-pl(t)) (2)
GEB-MAC E, ?l ? E Al, Ull ? E
9
EB-MAC Game
  • Theorem 1 Utility function is expected net
    reward (expected reward minus expected cost) that
    link can obtain from its transmission
  • where
  • Furthermore, there exits a Nash equilibrium
    characterized by

Ul(p)R(pl) S(p) - C(pl) F(p) ? l
S(p) pl ?n ? LtoI(l)(1-pn) probability of
transmission success
F(p) pl (1- ?n ? LtoI(l)(1-pn)) probability
of transmission failure
R(pl) pl(1/2plmax 1/3 pl) reward for
transmission success
C(pl) 1/3 (1- ?l) pl2 cost for transmission
failure
10
EB protocol as a stochastic subgradient algorithm
  • Theorem 2 The EB protocol described by (1) is a
    stochastic subgradient algorithm to maximize
    utility functon Ul

11
Uniqueness and Convergence of Nash Equilibrium
  • Define best response function as
  • Assume that
  • all links have same pmax and pmin
  • pmax lt 1 and pmin 0
  • Theorem If , then
  • Nash equilibrium is unique
  • From any initial point, iteration by best
    response converges to unique equilibrium
  • where K maxlLtoI(l)

pl(t1) argmaxplmin ? pl ? plmax Ul(pl,p-l(t))
12
Stochastic Subgradient vs. Best Response
  • Define a new update algorithm for link l as
  • vl(t) stochastic subgradient
  • ?l(t) step size
  • Theorem 6 The updates above converge to best
    response solution of user l under fixed p-l with
    probability 1 if all the following conditions
    hold
  • Step size ?(t) satisfies ?(t) ? 0, ?t0??(t)
    ?, ? t0??2(t) lt?, e.g., ?(t)1/t
  • Modified minimum persistent probability
    plminpmax( 1-pmin)Ml/1-?(1-( 1-pmin)Ml? pmin
  • Values of pmin, pmax and ? satisfy
    (1-?)/?(1/(1pmax)Ml-2/(1-pmin)Ml)?1, where
    MlLtoI(l) is the number of interfering links
    with link l

pl( t1) maxplmin,min plmax,pl(t) ?l(t)
vl(t)
13
Stochastic Subgradient vs. Best Response
The minimum value of ? that satisfies condition 3
of Theorem 6 vs. the number of interfering links
Ml with an infrared physical layer in 802.11
14
Numerical Results
Figure 1. A network with six links
15
Numerical Results of Link 1
Comparison of trajectories of pl(t) in the
network in Figure 1
16
Conclusion and Future Work
  • Reverse engineering for EB MAC protocol
  • Non-cooperative game model
  • Each link tries to maximize its utility in form
    of net reward for successful transmission using
    stochastic subgradient algorithm
  • Nash equilibria exist but, in general, no
    guarantee for uniqueness and convergence
  • showed conditions for uniqueness and convergence
  • Future work
  • Efficiency loss analysis
  • Reverse engineering CSMA/CA
  • Stochastic effects such as arrival statistics
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