When rate of interferer

1
Encoding Against an Interferers Codebook
Ivana Maric, Nan Liu and Andrea Goldsmith
Summary
System Model
Introduction
Motivation
Encoding Against an Interferers Codebook
ACHIEVEMENT DESCRIPTION

• Capacity of the channel with random states
  noncausally known at the encoder is obtained by
  Gelfand-Pinsker precoding against interference
  scheme
• For a network with one cognitive and one
  noncognitive pair, we have previously developed
  cognitive encoding strategies that bring gains,
  under the assumption of noncausal message
  knowledge at the cognitive encoder
• Such knowledge can be obtained through decoding,
  or through cooperation with noncognitive encoder
• This work focuses on communication of the
  cognitive radio pair while treating the
  noncognitive transmitter as an interferer
• We assume that we dont have the freedom to
  design the interferers codebook
• Codebook is already chosen to be i.i.d. or is a
  superposition codebook
• Our goal is to exploit the structure of the
  interference (codebook of the interferer) for
  rate gains and to consider the impact of delay in
  learning interferers message at the cognitive
  encoder

• Cognitive radios have ability to obtain (through
  sensing) and exploit (through advanced
  processing) information about communications in
  their vicinity
• Due to advanced technology, the cognitive
  encoder can use sophisticated encoding schemes to
  improve the network performance
• Due to their capabilities, cognitive radios can
  coexist with noncognitive users and thus improve
  spectral usage of the spectrum
• Capacity of cognitive radio networks are in
  general unknown
• In information theoretic approach, cognitive
  capabilities are modeled as a side information at
  the cognitive encoder about the transmissions in
  its vicinity
• Cognitive encoding strategies will depend on the
  amount of side information available

MAIN RESULTS Demonstrated that exploiting the
structure of interference can bring higher gains
for cognitive communications. Evaluated these
gains for a specific channel. Derived two outer
bounds on the performance. Analyzed cases with
and without delay in side information knowledge.
Showed that impact of delay differs depending
whether the interference is i.i.d. or has a
structure. HOW IT WORKS Without delay, the
encoder uses Gelfand-Pinsker precoding or, if
interferers rate is small, it forwards the
interfering message enabling the receiver to
decode it. With delay, it attempts to decode the
interferers message and then use cognitive
encoding strategies. ASSUMPTIONS AND
LIMITATIONS The noncausal knowledge assumption
is in general too optimistic. Single letter rate
characterizations are difficult to obtain due to
the structure of interference.
Capacity of networks with cognitive users are
unknown and, consequently, so are the optimal
ways in which to operate these networks Majority
of current information-theoretic models for
cognitive capabilities of the nodes are somewhat
idealistic

• Evaluate the outer bound
• Generalize observations to networks with
  cognitive and noncognitive users

END-OF-PHASE GOAL
STATUS QUO

• uniformly takes a row of a randomly
  generated codebook
• Codebook of i.i.d. structure
• Codebook of superposition structure

Structure of the interferers codeword
transmitted by a node in vicinity can be
exploited for higher rates at the cognitive
node. Delay has a different impact depending on
whether the interference is i.i.d. or a codeword
of an interferer.
COMMUNITY CHALLENGE

Prize level Capacity results for networks with
cognitive and noncognitive users
NEW INSIGHTS

• More realistically encoder knows through
  noisy channel
• Encoding at time depend on and

By exploiting the structure of the interference
created by the nodes in its vicinity, cognitive
nodes can achieve higher rates
Superposition Codebook
Example
Gelfand-Pinsker with Codebook
Capacity Definitions

• When the interferer uses a superposition coding,
  the cognitive user can improve its rate
• It decodes the codebook (the cloud) of the lower
  rate R1s and uses Gelfand-Pinsker encoding
  against the higher rate codebook. The following
  rate is achievable

• Interference degradation depends on realization
  of codebook
• Definition 1
• Communication rate same for any realization
• Probability of error different for different
  realizations
• Rate can be supported by some realizations
• supremum over all rate supported by
  majority
• Definition 2
• Allow communication rate to differ for each
  realization
• There is a capacity associated with each
  realization
• the capacity that can be supported by
  majority

Lemma 2 Achievable rate
Lemma 1 Achievable rate
for joint distribution that factors as

• When rate of interferers codebook small
• Does not place burden for destination to decode
  interference
• When rate of interferers codebook large
• Treating it as i.i.d. sequence and use
  Gelfand-Pinsker

• x is a deterministic function of (v, u, xs)
• is given by the interferer

• Taking into account that the state is a codebook
  helps
• Forwarding interference can outperform GP
  precoding

Theorem 1

• Rates of Lemma 1 are then a special case when
  V0 (no decoding) or Xs0 (full decoding)

Interferer Codeword with Delay and Noise
Future Work
I.I.D. Sequence with Delay
Conclusions

• Studied cognitive radio from novel and realistic
  perspectives
• Primary user is not willing to perform joint
  codebook design
• Primary user uses a randomly generated codebook
• codebook structure i.i.d. or superposition
• Cognition is achieved through delay and noise
• Provided capacity definitions for random
  interferers codebook
• Proposed achievability schemes under various
  scenarios
• Showed that taking into account interference
  comes from a codebook helps
• Proved that structured interferers codebook is
  helpful
• In the more realistic scenario cognition
  through delay and noise
• In the case of i.i.d. sequence, delayed
  cognitionno cognition
• Delayed cognition is still useful when state is
  a codeword

Gelfand-Pinsker with codebook stage
Noncognitive stage

• Decoding the other users message introduces
  delay in the availability of side information at
  the cognitive encoder
• We first analyze the case when
• Xifi(W, S1, , Si-1)
• We have the following

• Encoder splits its message into two parts
  and
• First symbols, sends as if does not
  know channel state
• Encoder is able to decode state sequence after
  symbols
• For the remaining symbols, send
  using Lemma 1

• Evaluate the obtained upper bounds
• Use the obtained insights to design networks
  with cognitive and noncognitive users

Lemma 3 The capacity is

• Lemma 2 implies that the rate equals the rate
  without side information at the encoder
• i.i.d. side information obtained with delay does
  not help