12 research outputs found
The Zero-Undetected-Error Capacity Approaches the Sperner Capacity
Ahlswede, Cai, and Zhang proved that, in the noise-free limit, the
zero-undetected-error capacity is lower bounded by the Sperner capacity of the
channel graph, and they conjectured equality. Here we derive an upper bound
that proves the conjecture.Comment: 8 Pages; added a section on the definition of Sperner capacity;
accepted for publication in the IEEE Transactions on Information Theor
Active sequential hypothesis testing
Consider a decision maker who is responsible to dynamically collect
observations so as to enhance his information about an underlying phenomena of
interest in a speedy manner while accounting for the penalty of wrong
declaration. Due to the sequential nature of the problem, the decision maker
relies on his current information state to adaptively select the most
``informative'' sensing action among the available ones. In this paper, using
results in dynamic programming, lower bounds for the optimal total cost are
established. The lower bounds characterize the fundamental limits on the
maximum achievable information acquisition rate and the optimal reliability.
Moreover, upper bounds are obtained via an analysis of two heuristic policies
for dynamic selection of actions. It is shown that the first proposed heuristic
achieves asymptotic optimality, where the notion of asymptotic optimality, due
to Chernoff, implies that the relative difference between the total cost
achieved by the proposed policy and the optimal total cost approaches zero as
the penalty of wrong declaration (hence the number of collected samples)
increases. The second heuristic is shown to achieve asymptotic optimality only
in a limited setting such as the problem of a noisy dynamic search. However, by
considering the dependency on the number of hypotheses, under a technical
condition, this second heuristic is shown to achieve a nonzero information
acquisition rate, establishing a lower bound for the maximum achievable rate
and error exponent. In the case of a noisy dynamic search with size-independent
noise, the obtained nonzero rate and error exponent are shown to be maximum.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1144 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Error-and-Erasure Decoding for Block Codes with Feedback
Inner and outer bounds are derived on the optimal performance of fixed length
block codes on discrete memoryless channels with feedback and
errors-and-erasures decoding. First an inner bound is derived using a two phase
encoding scheme with communication and control phases together with the optimal
decoding rule for the given encoding scheme, among decoding rules that can be
represented in terms of pairwise comparisons between the messages. Then an
outer bound is derived using a generalization of the straight-line bound to
errors-and-erasures decoders and the optimal error exponent trade off of a
feedback encoder with two messages. In addition upper and lower bounds are
derived, for the optimal erasure exponent of error free block codes in terms of
the rate. Finally we present a proof of the fact that the optimal trade off
between error exponents of a two message code does not increase with feedback
on DMCs.Comment: 33 pages, 1 figure
Bit-wise Unequal Error Protection for Variable Length Block Codes with Feedback
The bit-wise unequal error protection problem, for the case when the number
of groups of bits is fixed, is considered for variable length block
codes with feedback. An encoding scheme based on fixed length block codes with
erasures is used to establish inner bounds to the achievable performance for
finite expected decoding time. A new technique for bounding the performance of
variable length block codes is used to establish outer bounds to the
performance for a given expected decoding time. The inner and the outer bounds
match one another asymptotically and characterize the achievable region of
rate-exponent vectors, completely. The single message message-wise unequal
error protection problem for variable length block codes with feedback is also
solved as a necessary step on the way.Comment: 41 pages, 3 figure
The Sphere Packing Bound via Augustin's Method
A sphere packing bound (SPB) with a prefactor that is polynomial in the block
length is established for codes on a length product channel
assuming that the maximum order Renyi capacity among the component
channels, i.e. , is . The
reliability function of the discrete stationary product channels with feedback
is bounded from above by the sphere packing exponent. Both results are proved
by first establishing a non-asymptotic SPB. The latter result continues to hold
under a milder stationarity hypothesis.Comment: 30 pages. An error in the statement of Lemma 2 is corrected. The
change is inconsequential for the rest of the pape