Grassmann Manifold, Er Barg, Senior Member, Dmitry Yu. Nogin
In[1], the density of the Haar measure for the case of q�Y� @ A was cited incorrectly from [2, eq. (A18)]. The corrections affect the last displayed equationbefore (10) which should have the form
A 2002 A low-rate bound on the reliability of a quantum discrete memoryless channel (2008)
Abstract—We extend a low-rate improvement of the random coding bound on the reliability of a classical discrete memoryless channel (DMC) to its quantum counterpart. The key observation that we make...
Estimates of the distance distribution of codes and designs (2008)
Alexei Ashikhmin, Er Barg, Simon Litsyn, Senior Member, Senior Member
Abstract—We consider the problem of bounding the distance distribution for unrestricted block codes with known distance and/or dual distance. Applying the polynomial method, we provide a general...
Er Barg, Senior Member, Gilles Zémor, G. C. Temes, Oversampling Delta–sigma Data
band-limited functions. The decoders are still convolutional, and thus democratic; in his construction, the rate of the exponential decay of the error, shown here to be necessarily strictly inferior...
Concatenated codes: serial and parallel (2005)
Er Barg, Senior Member, Gilles Zémor
Abstract—An analogy is examined between serially concatenated codes and parallel concatenations whose interleavers are described by bipartite graphs with good expanding properties. In particular, a...
Digital fingerprinting codes: Problem statements, constructions, identification of traitors (2003)
Er Barg, Senior Member, G. R. Blakley, Grigory A. Kabatiansky
Abstract—We consider a general fingerprinting problem of digital data under which coalitions of users can alter or erase some bits in their copies in order to create an illegal copy. Each user is...
Random Codes: Minimum Distances and Error Exponents (2002)
Er Barg, Senior Member, G. David Forney
Abstract—Minimum distances, distance distributions, and error exponents on a binary-symmetric channel (BSC) are given for typical codes from Shannon’s random code ensemble and for typical codes...
Bounds on packings of spheres in the Grassmann manifold (2002)
Er Barg, Senior Member, Dmitry Yu. Nogin
bounds for packings of spheres (codes) in the Grassmann manifolds over and. Asymptotic expressions are obtained for the geodesic metric and projection Frobenius (chordal) metric on the manifold....
A new upper bound on the reliability function of the Gaussian Channel (2000)
Alexei E. Ashikhmin, Er Barg, Simon N. Litsyn, Senior Member
Abstract—We derive a new upper bound on the exponent of error probability of decoding for the best possible codes in the Gaussian channel. This bound is tighter than the known upper bounds (the...
Tilborg, On the complexity of minimum distance decoding of long linear codes (1999)
Er Barg, Evgueni Krouk, Senior Member
Abstract — We suggest a decoding algorithm of -ary linear codes, which we call supercode decoding. It ensures the error probability that approaches the error probability of minimumdistance...