Related papers: A Refinement of Expurgation
In this paper, we derive analytic expressions for the success probability of decoding (Partial) Unit Memory codes in memoryless channels. An applications of this result is that these codes outperform individual block codes in certain…
We consider upper bounds on the error probability in channel coding. We derive an improved maximum-likelihood union bound, which takes into account events where the likelihood of the correct codeword is tied with that of some competitors.…
In continuation to an earlier work, where error exponents of typical random codes were studied in the context of general block coding, with no underlying structure, here we carry out a parallel study on typical random, time-varying trellis…
We derive various error exponents in the bee identification problem under two different decoding rules. Under na\"ive decoding, which decodes each bee independently of the others, we analyze a general discrete memoryless channel and a…
We introduce an expurgation method for source coding with side information that enables direct dual-domain derivations of expurgated error exponents. Dual-domain methods yield optimization problems over few parameters, with any sub-optimal…
This paper presents an achievability bound that evaluates the exact probability of error of an ensemble of random codes that are decoded by a minimum distance decoder. Compared to the state-of-the-art which demands exponential computation…
This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length or maximum redundancy and average redundancy, including a convex combination of the…
This paper studies several properties of channel codes that approach the fundamental limits of a given (discrete or Gaussian) memoryless channel with a non-vanishing probability of error. The output distribution induced by an…
We consider the problem of inferring the probability distribution associated with a language, given data consisting of an infinite sequence of elements of the languge. We do this under two assumptions on the algorithms concerned: (i) like a…
A Lagrange-dual (Gallager-style) lower bound is derived for the error exponent function of the typical random code (TRC) pertaining to the i.i.d. random coding ensemble and mismatched stochastic likelihood decoding. While the original…
We derive an exponentially decaying upper-bound on the unnormalized amount of information leaked to the wire-tapper in Wyner's wire-tap channel setting. We characterize the exponent of the bound as a function of the randomness used by the…
A rate-dependent upper bound of the best achievable block error probability of polar codes with successive-cancellation decoding is derived.
We address the problem of bounding below the probability of error under maximum likelihood decoding of a binary code with a known distance distribution used on a binary symmetric channel. An improved upper bound is given for the maximum…
We consider ensembles of channel codes that are partitioned into bins, and focus on analysis of exact random coding error exponents associated with optimum decoding of the index of the bin to which the transmitted codeword belongs. Two main…
This paper is devoted to the structure of the complete asymptotic expansion of the probability that a large combinatorial object is irreducible or consists of a given number of irreducible parts, where irreducibility is understood in terms…
We study the universal attainability of the expurgated error exponent for discrete memoryless channels (DMCs). While the random-coding exponent is known to be universally attainable via maximum mutual information (MMI) decoding for DMCs, it…
Past works on remote lossy source coding studied the rate under average distortion and the error exponent of excess distortion probability. In this work, we look into how fast the excess distortion probability converges to 1 at small rates,…
The error exponent of the typical random code is defined as the asymptotic normalized expectation of the logarithm of the probability of error, as opposed to the traditional definition of the random coding exponent as the normalized…
In this work we show how an improved lower bound to the error exponent of the memoryless multiple-access (MAC) channel is attained via the use of linear codes, thus demonstrating that structure can be beneficial even in cases where there is…
After a recollection on compression through a projection onto a polyhedral set (which generalizes the compression by coordinates quantization), we express, in this framework, the probability that an image is coded with $K$ coefficients as…