Encoding Against an Interferer’s Codebook
Ivana Maric, Nan Liu and Andrea Goldsmith
Summary
Capacity of networks with
cognitive users are unknown and,
consequently, so are the optimal
ways in which to operate these
networks
Majority of current informationtheoretic models for cognitive
capabilities of the nodes are
somewhat idealistic
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.
END-OF-PHASE GOAL
STATUS QUO
ACHIEVEMENT DESCRIPTION
HOW IT WORKS:
Structure of the
interferer’s 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.
With delay, it attempts to decode the
interferer’s 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.
COMMUNITY CHALLENGE
NEW INSIGHTS
Without delay, the encoder uses Gel’fandPinsker precoding; or, if interferer’s rate is
small, it forwards the interfering message
enabling the receiver to decode it.
•Evaluate the outer
bound
• Generalize
observations to
networks with
cognitive and
noncognitive users
Prize level: Capacity
results for networks with
cognitive and
noncognitive users
• 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
By exploiting the structure of the interference created by the nodes in its vicinity, cognitive
nodes can achieve higher rates
Capacity Definitions
Gel’fand-Pinsker with Codebook
• 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
• C1 : supremum over all rate supported by majority
Lemma 1: Achievable rate
•Definition 2
max max{min{ I ( X ; Y | S ), I (U , S ; Y )  Rs },
p ( u|s ), f ()
• Allow communication rate to differ for each realization
I (U ; Y )  I (U ; S )}
• There is a capacity associated with each realization
• When rate of interferer’s codebook small
• C2: the capacity that can be supported by majority
• Does not place burden for destination to decode interference
Theorem 1 :
• When rate of interferer’s codebook large
C1  C2  C
• Treating it as i.i.d. sequence and use Gel’fand-Pinsker
I.I.D. Sequence with Delay
Interferer Codeword with Delay and Noise
n  n1
n1
Noncognitive stage
• Decoding the other user’s message introduces delay in the
availability of side information at the cognitive encoder
• We first analyze the case when
Xi=fi(W, S1, …, Si-1)
• We have the following:
Lemma 3: The capacity is
C  max I ( X ; Y )
p( x)
• 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
Gel’fand-Pinsker with codebook stage
• Encoder splits its message into two parts W1 and W2
• First n1 symbols, sends W1 as if does not know channel state
• Encoder is able to decode state sequence after n1 symbols
Rs
n1

n I (S ; Z )
• For the remaining n  n1 symbols, send W2 using Lemma 1
System Model
Introduction
Motivation
Encoding Against an Interferer’s Codebook
• Capacity of the channel with random states noncausally
known at the encoder is obtained by Gel’fand-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
• S n uniformly takes a row of a randomly generated codebook
noncausal message knowledge at the cognitive encoder
• Codebook of i.i.d. structure
• Such knowledge can be obtained through decoding, or
through cooperation with noncognitive encoder
• Codebook of superposition structure
• This work focuses on communication of the cognitive radio
pair while treating the noncognitive transmitter as an
S
interferer
•
• We assume that we don’t have the freedom to design the
interferer’s codebook
n
S
•
More
realistically:
encoder
knows
through noisy channel
•Codebook is already chosen to be i.i.d. or is a
superposition codebook
• Encoding at time i depend on W and Z1 , Z 2 ,, Z i 1
• 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 interferer’s message at the
cognitive encoder
n
Example
Superposition Codebook
• 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 Gel’fand-Pinsker encoding against the higher rate codebook.
The following rate is achievable:
Lemma 2: Achievable rate
R  I (U ; Y | V )  I (U ; X S | Y )
R  R1s  I (V ,U ; Y )  I (U ; X s | V )
for joint distribution that factors as p(u | v) p( y | x, xs )
• Taking into account that the state is a codebook helps
• Forwarding interference can outperform GP precoding
• x is a deterministic function of (v, u, xs)
• p(v) p( xs | v) is given by the interferer
• Rates of Lemma 1 are then a special case: when V=0 (no decoding)
or Xs=0 (full decoding)
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 interferer’s codebook
• Proposed achievability schemes under various scenarios
• Showed that taking into account interference comes from a codebook helps
• Proved that structured interferer’s codebook is helpful
• In the more realistic scenario: cognition through delay and noise
• In the case of i.i.d. sequence, delayed cognition=no cognition
• Delayed cognition is still useful when state is a codeword
Future Work
• Evaluate the obtained upper bounds
• Use the obtained insights to design networks
with cognitive and noncognitive users