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

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

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;

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]

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

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

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.

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

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