Superposition encoding

1
Interference Channels with Receiver Side
Information
Nan Liu, Deniz Gunduz, Andrea Goldsmith and H.
Vincent Poor
Desired Source Results
Desired Source Channel Model
Introduction
Interference Channels with Correlated Receiver
Side Information
ACHIEVEMENT DESCRIPTION
MAIN RESULT When receiver side information is
about the desired source, separation is optimal.
When receiver side information is about the
interfering source, a general joint
source-channel coding strategy is proposed. The
optimality of separation as well as necessary and
sufficient conditions for reliable transmission
is characterized for certain special cases. HOW
IT WORKS The main aim of the network is still
to reduce interference caused to the other
transmitter-receiver pair. Hence, it is best to
transmit only what the receiver doesnt know.
When the other receiver has some side
information, since this part of the knowledge
does not cause interference, include it in the
part of interference the other receiver decodes.
ASSUMPTIONS AND LIMITATIONS Due to the
difficulty of finding capacity results for the
interference channel, tight results are only
possible in special cases.

• Expand the definition of separation and
  re-explore the optimality of separation
• Generalize our tight results to include all ICs
  where superposition encoding is optimal

Provides several new results regarding the joint
source-channel coding of interference channel
with receiver side information. While the
achievable strategy is general, sufficient and
necessary conditions exist only in special cases.

• Multiple communication systems operating
  simultaneously causes interference
• In applications such as sensor networks, it is
  reasonable to assume that the receivers have
  access to their own correlated observations about
  the underlying source sequences as well
• Traditional interference channel (IC) excludes
  this possibility, and hence, we study
  interference channel with receiver side
  information
• Receiver side information about desired source
• Receiver side information about interfering
  source
• The goal understanding how to fully take
  advantage of side information at the receiver to
  reduce interference

Theorem 1 Separation is optimal, i.e., necessary
and sufficient condition for
reliable transmission is
END-OF-PHASE GOAL
where is the capacity region of the
interference channel.
STATUS QUO

• Separation is optimal
• Transmitters first apply Slepian-Wolf source
  coding
• Then use optimal IC code to transmit compressed
  bits
• No single-letter characterization for capacity
  region of IC
• Still can prove optimality of separation using
  n-letter forms

It is best to transmit only what the receiver
doesnt know, and also include as much as
possible the side information the other receiver
knows.

• Two source-side information pairs are
  independent
• Side information is about the desired source
• How to utilize the side information to reduce
  the interference to the other transmitter-receiver
  pair

COMMUNITY CHALLENGE
The impact of receiver side information on larger
networks
NEW INSIGHTS
The result provides intuition as to how to
utilize side information at the receiver to
reduce interference
Deterministic Side Information
IC with Message Side Information
Joint Source-Channel Coding Strategy
Interfering Source Channel Model
Theorem 2 Separation is optimal, i.e., necessary
and sufficient condition for
reliable transmission is

• Separation is optimal
• Encode side information into one message
• Encode remaining information into another
  message
• Transmit the two messages using an optimal code
  for IC with message side information
• is the capacity region of IC with message
  side info

• Superposition encoding
• A distorted version of is
• is encoded into the inner codebook
• Receiver 2 decodes using received signal
  and its side information
• Decoding part of the interference helps decoding
  the desired source

• More general than classical IC
• In general, no single-letter expression for
  capacity region
• We provide an n-letter form of the capacity
  region
• We prove the optimality of separation using
  n-letter forms

• Two source-side information pairs are
  independent
• Side information is about the interfering source
  
• How the side information about the interference
  helps in decoding the desired information

Insights and Future Work
Conclusions
Necessary and Sufficient Conditions
Z-channel with Degraded Message Sets

• Study the problem of joint source-channel coding
  in transmitting independent sources over IC with
  receiver side info
• Side information about desired source
• Separation is optimal
• Transmit only bits the receiver does not know to
  reduce interference to the other
  transmitter-receiver pair
• Side information about interfering source
• Proposed joint source-channel coding strategy
• Separation is optimal with deterministic side
  information
• Complete solution for a special case
• As a byproduct, capacity region for a class of
  Z-channels with degraded message sets

• Insights
• Transmit only the bits the receiver does not
  know
• Include the side information of the interfering
  receiver as much as possible into the message
  intended for both receivers
• Future work
• Expand the definition of separation to include
  disjoint source- channel distribution
• Re-explore optimality of separation under these
  new definitions
• Explore the possibility that the joint
  source-channel coding strategy is tight for all
  ICs where superposition encoding is optimal
• Apply the insights of using side information to
  reduce interference to larger wireless networks

• For special cases, single-letter expression of
  can be found
• Necessary and sufficient condition described in
  single-letter form, yielding a complete solution
• Superposition encoding is optimal for the
  underlying IC
• Superposition encoding is shown to be still
  optimal with message side information
• Joint source-channel coding strategy is optimal

• Z-interference channel with message side
  information is very much related to Z-channel
  with degraded message sets, Kramer/Shamai 07
• Characterize the capacity region for a class of
  Z-channels with degraded message sets