Unequal Error Protection: Application and Performance Limits

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Unequal Error Protection Application and
Performance Limits
S. Borade, B. Nakiboglu, L. Zheng

• bits as the universal measure of information
  and interface to physical layer a homogenous
  view.
• High priority control messages are sent over
  separated channels.
• No performance limits on UEP
• Perfect reliability assumed on network controls

• Complete UEP tradeoff with geometric approach
• Data driven network controls, Layering and QoS
  as interface

• MAIN RESULT
• Optimizing the overall resource, the reliability
  of control signals has a threshold effect
• Communicating at capacity, not even a single bit
  can be protected with positive exponent
• Message-wise prioritization yields better
  tradeoffs than bit-pipe partitioning.
• HOW IT WORKS
• Protecting special message is much easier than
  special bit
• With feedbacks, a two-phase scheme can be used,
  where critical message is used to initiate
  retransmissions

New interface to the physical layer leads to more
flexible higher layer functionalities, and system
level optimizations the new interface also needs
to be backward compatible to bit based networks

• Joint coding allows flexible resource
  allocation
• Priority of critical data in the form/costs of
  better error protections
• Global optimization of resource allocation among
  heterogeneous data

Better tradeoff in UEP has significant effects on
overall system performance
Embedding control messages/significant data with
UEP
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Motivating Example Why UEP?

• Heterogeneous nature of data in MANETS
• Significant control overhead, with delay and
  reliability requirements
• Evolving and imperfect reliability of data due
  to short codes
• Hierarchical cooperation differentiate local and
  global data exchanges
• Prioritizing of error protections reflects on
  overall resource allocations.
• Overhead in controlling the service rate of a
  queue
• reporting of queue lengths
• switching between high and low service rates
• Cost of control messages

• Threshold effect in minimizing overflow
  probability imperfect controls useful for highly
  dynamic system

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UEP the Formulation

• Conventional approach separate channel for
  different types of data

• Joint coding more flexible allocation of error
  protection capability

• Main challenges
• optimizing input distribution
• computing the resulting tradeoff (R1, R2, E1,
  E2), multi-message error exponents
• practical code designs beyond linear codes

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Protecting a single special bit
Special bits -- minimize -- while sending
normal data reliably Can We communicate at
capacity, while protecting one special bit with
positive error exponent? Proof Blowing up
Lemma Ahlswede-Gacs-Korner76
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Message-wise UEP

• Protection of a special message (codeword)
• Messages too costly to miss
• system emergency, critical command
• Minimize
• Messages too costly to implement
• irreversible actions, format disk
• Minimize

Can We communicate at capacity, while protecting
one special message with positive error exponent?
Theorem
where is capacity achieving output
distribution, achieved by sending special message
with
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Many Special Messages

• First messages special. Total
  messages for
• Definition is best exponent
  when communicating reliably close to capacity
• each special message
  .
• If only special messages achieve classical error
  exponent

With additional ordinary messages,
Special messages optimal reliability Ordinary
messages optimal data-rate
Theorem
Bottom line messages are much easier to protect
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Using Special Messages the Feedback Example

• Using special message to initiate retransmission

Channel
Decoder
Encoder

• With multiple special bits
• First phase transmit special bits at capacity
• If correct, send the rest of bits, otherwise use
  special message to signal retransmission
• Achieves the linear rate-reliability tradeoff
• Can generalize to multiple levels of priority
• Shown to be the optimal tradeoff.

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UEP for Very Noisy Channels

• Local approximation of K-L divergence
• With joint encoding, achievable
  iff
• Comparing to bit-pipe partitioning, with a,
  (1-a) fractions of bandwidth allocation
• Generalizations to global geometry.

Finding the optimal input distribution
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Looking Ahead

• New interface to the physical layer
• More than one type of data, more than one type
  of error
• Allowing higher layer to directly control and
  allocate the capability of error protections
• Unifying data and control, local and global
  data, prioritization according to evolving
  reliabilities
• Natural QoS implementation
• Geometric Analysis local to global
  generalization
• The challenge of practical code designs.