12 research outputs found
Asymmetric Evaluations of Erasure and Undetected Error Probabilities
The problem of channel coding with the erasure option is revisited for
discrete memoryless channels. The interplay between the code rate, the
undetected and total error probabilities is characterized. Using the
information spectrum method, a sequence of codes of increasing blocklengths
is designed to illustrate this tradeoff. Furthermore, for additive discrete
memoryless channels with uniform input distribution, we establish that our
analysis is tight with respect to the ensemble average. This is done by
analysing the ensemble performance in terms of a tradeoff between the code
rate, the undetected and the total errors. This tradeoff is parametrized by the
threshold in a generalized likelihood ratio test. Two asymptotic regimes are
studied. First, the code rate tends to the capacity of the channel at a rate
slower than corresponding to the moderate deviations regime. In this
case, both error probabilities decay subexponentially and asymmetrically. The
precise decay rates are characterized. Second, the code rate tends to capacity
at a rate of . In this case, the total error probability is
asymptotically a positive constant while the undetected error probability
decays as for some . The proof techniques involve
applications of a modified (or "shifted") version of the G\"artner-Ellis
theorem and the type class enumerator method to characterize the asymptotic
behavior of a sequence of cumulant generating functions.Comment: 28 pages, no figures in IEEE Transactions on Information Theory, 201
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
Expurgated random-coding ensembles: Exponents, refinements, and connections
This paper studies expurgated random-coding bounds and exponents with a given (possibly suboptimal) decoding rule. Variations of Gallagerâs analysis are presented, yielding new asymptotic and non-asymptotic bounds on the error probability for an arbitrary codeword distribution. A simple non-asymptotic bound is shown to attain an exponent which coincides with that of CsiszĂĄr and Körner for discrete alphabets, while also remaining valid for continuous alphabets. The method of type class enumeration is studied for both discrete and continuous alphabets, and it is shown that this approach yields improved exponents for some codeword distributions. A refined analysis of expurgated i.i.d. random prefactor, thus improving on Gallagerâs O(1) prefactor. coding is given which yields an exponent with a O ( 1 ân I