1. Unequal Error Protection: Application and Performance Limits
S. Borade, B. Nakiboglu, L. Zheng
END-OF-PHASE GOAL
COMMUNITY CHALLENGE
ACHIEVEMENT DESCRIPTION
STATUS QUO
NEW INSIGHTS
“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;
What technical challenge is being undertaken on behalf of the project
The notion of unequal protection tries to distinguish one type of data from another, which is directly opposite from Shannon’s view that all information should be treated equally. Moreover, the priority here is measured in error probability, which is again different from the conventional view that information should be reliably transmitted. Both require some new formulation and new analytical tools to be addressed.
2. Why is it hard and what are the open problems
Error exponent is a hard problem by itself. Instead of talking about the typical behavior of the channels, which is only meaningful in static problems, we address the variation of the empirical realization of the channel noise. The problem is thus dynamic in nature. It translates the dynamic environment, including mobility and change of network topology, into the dynamics in distributions. This is quite different from the conventional approaches.
3. How has this problem been addressed in the past
There has been a number of designs of UEP codes, but the performance limits are hard to derive. The practical use of UEP is limited mostly to Gaussian superposition, which is an almost trivial case.
4. What new intellectual tools are being brought to bear on the problem
Mainly, two new tools are involved here. In the proof of the converse, we need some combinatorics, and in the optimization of the input distributions, we used information geometry. Conceptually, we ask the question of how to measure partial information, which turns out to suggest that “bit” should not be the universal metric in dynamic problems. This deviate from the conventional view, and post a set of new problems.
5. What is the main intermediate achievement
We derived some new bounds on UEP tradeoff, and demonstrated that such new tradeoff can have significant impact in overall system resource allocations.
6. How and when does this achievement align with the project roadmap(end-of-phase or end-of-project goal)
We are making good progress towards a complete characterization of the UEP performance limits, and are starting to address the new network optimization problems when physical layers are accessed with the new interface with heterogeneous data types.
7. What are the even long-term objectives and consequences?
Our formulation leads to many new network optimization problems. The analytical techniques involved, mainly the geometric analysis, can be developed into the new key tools to study cooperative communication problems.
8. Which thrusts and SOW tasks does this contribution fit under and why?
The use of UEP codes naturally allow some of the traditionally higher layer optimizations to be done with new physical layer capability. This falls into our general vision of cross-layer designs. The gain resulted can be an important part contributing towards the system performance improvement that project is aimed at.
Better tradeoff in UEP has significant effects on overall system performance
Embedding control messages/significant data with UEP

2. 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 μ λ 1 2
Observer
Threshold effect in minimizing overflow probability: imperfect controls useful for highly dynamic system

3. 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;

4. 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-Korner’76]
Theorem:
[Borade-Nakiboğlu-Zheng]

5. 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
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

6. Bottom line: messages are much easier to protect
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,
Theorem:
Special messages: optimal reliability
Ordinary messages: optimal data-rate
Bottom line: messages are much easier to protect

7. Using Special Messages: the Feedback Example
Using special message to initiate retransmission
Channel
Encoder
Decoder
If correct, send other bits. Else, special buzzer message
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.

8. UEP for Very Noisy Channels
Local approximation of K-L divergence:
With joint encoding, achievable iff
Comparing to bit-pipe partitioning, with α, (1-α) fractions of bandwidth allocation
Generalizations to global geometry.
Finding the optimal input distribution

9. Looking Ahead Physical layer 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.
Physical layer
Platinum bits
Silver bits
Gold bits
Economy bits