We aim to exploit cognition to maximize network performance

1
The Capacity Region of the Cognitive
Z-interference Channel with a Noiseless
Non-cognitive Link
Nan Liu, Ivana Maric, Andrea Goldsmith and Shlomo
Shamai (Shitz)
Summary
Motivation
Introduction
Previous Work

• In multiuser networks
• A key issue is how to handle and exploit
  interference created by simultaneous
  transmissions
• Not well understood
• Capacity of the interference channel an open
  problem
• Capacity of the Z-interference channel an open
  problem
• Cognitive radio networks
• Multiuser networks in which some users cognitive,
  i.e., can sense the environment and hence obtain
  side information about transmissions in
  neighborhood
• How to exploit cognition in optimal ways?

• We aim to exploit cognition to maximize network
  performance
• What is the side information at a cognitive node?
• What is the best encoding scheme given this side
  information?
• A model for cognition in IT
• Perfect side information at the cognitive pair
• Very optimistic
• Cognitive and non-cognitive pair communication
  modeled as

ACHIEVEMENT DESCRIPTION
Capacity of networks with cognitive users are
unknown. Consequently, optimal ways how to
operate such networks are not understood, nor it
is clear how cognitive nodes should exploit the
obtained information. IT channel models
suitable for networks with cognitive users still
need to be proposed. Capacity of Z-interference
channel is still unknown.

• Maric, Yates, Kramer, Devroye, Mitran, Tarokh
  2006
• Wu, Vishwanath, Arapostathis, Jovicic,
  Viswanath, Sridharan, Vishwanath 2007
• Maric, Goldsmith, Shamai, Kramer, Jiang, Xin,
  Cao, Chen 2008
• Capacity results known in special cases of
  strong and weak interference

MAIN ACHIEVEMENT 1) The capacity region of the
discrete cognitive Z- interference channel with a
noiseless non-cognitive link2) An inner and
outer bound for the cognitive Z-interference
channel 3) Solution to the generalized
Gelfand- Pinsker (GP) problem in which a
transmitter-receiver pair communicates in the
presence of interference non causally known to
the encoder. Our solution determines the optimum
structure of interference. HOW IT WORKS
Non-cognitive encoder uses superposition coding
to enable partial decoding of interference. The
cognitive encoder precodes against the rest of
interference using GP encoding. ASSUMPTIONS AND
LIMITATIONS The considered channel model

• 1) Optimal scheme for some channels
• 2) Superposition coding and Gelfand-Pinsker
  coding may be required in order to minimize
  interference, in some channels. This is in
  contrast to the Gaussian channel.
• 3) For the GP problem, the optimal interference
  has a superposition structure

IMPACT
STATUS QUO
source 1
dest1
dest2
source 2
In some scenarios, interference can be minimized
by exploiting the structure of interference and
cognition at the nodes. Cognition should be used
by the encoder to precode against part of the
interference caused to its receiver.

• Evaluate a numerical example
• Apply proposed encoding scheme to larger
  networks and to different cognitive node models

NEXT-PHASE GOALS
NEW INSIGHTS
Encoding scheme was proposed that exploits
cognition and is optimal in certain scenarios
Converse
Capacity Result
Achievability
Channel Model
Theorem Achievable rate pairs (R1,R2) are given
by a union of rate regions given by
Theorem Achievable rate pairs (R1,R2) belong to
a union of rate regions given by
Theorem For the cognitive ZIC with a noiseless
non-cognitive link i.e., p(y2x2) is a
deterministic one-to-one function, the capacity
region is given by the union of rate regions
?
where the union is over all probability
distributions p( v,u,x2 )p( x1 u,x2 )
where the union is over all probability
distributions p( v,u,x2 )p( x1 u,x2 )
where the union is over all probability
distributions p( v,u,x2 )p( x1 u,x2 )

• Two messages Rates

Encoding scheme Encoder 2 - rate-splits its
message into two messages -
encodes using superposition coding with
an inner codebook vn and an outer
codebook x2n Encoder 1 - for each vn it
performs binning, i.e., Gelfand-Pinsker
encoding in order to precode against
interference x2n given vn

• In general, the achievable rates and the
  converse result do no meet
• Markovity U?(V,X2)?Y2 implies
• I(UX2 V) I(UY2 V)
• For Y2X2 the two regions are the same. This
  leads to the following

• Encoding

• Decoding

• Alphabet for encoder t

• Encoder 1 is cognitive in the sense that it knows
  the message of other user

Summary and Future Work
Implications
Connection to the Gelfand-Pinsker Problem

• In the considered scenario, interference can be
  minimized by exploiting the structure of
  interference and cognition at the nodes
• The corresponding encoding scheme requires
• Superposition coding
• 2) Gelfand-Pinsker coding
• This is in contrast to the Gaussian case
• For the GP problem, the optimum interference has
  superposition structure
• We considered single-user cognitive models that
  capture delay in related work Maric, Liu and
  Goldsmith 2008

• An achievable rate region and an outer bound for
  the cognitive ZIC were derived
• The capacity result for the ZIC with a noiseless
  non-cognitive link was obtained
• The Generalized Gelfand-Pinsker problem was
  solved
• Future work
• Evaluate a numerical example
• Apply proposed encoding scheme to larger
  networks and to different cognitive node models

• In the cognitive ZIC, when X2Y2, X2 can be
  viewed as a state i.i.d. distributed on a set of
  size of 2nR2
• We can design not only the codebook of the
  cognitive encoder, but also the structure of the
  state

• Thus, for the given rate R2 of the interferer,
  the optimal interference has the superposition
  structure

• Communication in the presence of interference
  (state) non-causally known to the encoder