The Sphere Packing Bound for Memoryless Channels

Date

2020-07-01

Author

Nakiboğlu, Barış

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

192
views

0
downloads

Sphere packing bounds (SPBs)-with prefactors that are polynomial in the block length-are derived for codes on two families of memoryless channels using Augustin's method: (possibly nonstationary) memoryless channels with (possibly multiple) additive cost constraints and stationary memoryless channels with convex constraints on the composition (i.e., empirical distribution, type) of the input codewords. A variant of Gallager's bound is derived in order to show that these sphere packing bounds are tight in terms of the exponential decay rate of the error probability with the block length under mild hypotheses.

Subject Keywords

Computer Networks and Communications, Information Systems, Computer Science Applications

URI

https://hdl.handle.net/11511/63192

Journal

PROBLEMS OF INFORMATION TRANSMISSION

DOI

https://doi.org/10.1134/s0032946020030011

Collections

Department of Electrical and Electronics Engineering, Article

Suggestions

OpenMETU
Core

The Sphere Packing Bound via Augustin's Method Nakiboğlu, Barış (Institute of Electrical and Electronics Engineers (IEEE), 2019-02-01) A sphere packing bound (SPB) with a prefactor that is polynomial in the block length n is established for codes on a length n product channel W-[1,W- n], assuming that the maximum order 1/2 Renyi capacity among the component channels, i.e. max(t is an element of[1, n]) C-1/2, W-t, is O(ln n). 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 re...
A modular regularized variational multiscale proper orthogonal decomposition for incompressible flows Eroglu, Fatma G.; Kaya Merdan, Songül; Rebholz, Leo G. (Elsevier BV, 2017-10-01) In this paper, we propose, analyze and test a post-processing implementation of a projection-based variational multiscale (VMS) method with proper orthogonal decomposition (POD) for the incompressible Navier-Stokes equations. The projection-based VMS stabilization is added as a separate post-processing step to the standard POD approximation, and since the stabilization step is completely decoupled, the method can easily be incorporated into existing codes, and stabilization parameters can be tuned independe...
The DRBEM solution of incompressible MHD flow equations Bozkaya, Nuray; Tezer, Münevver (Wiley, 2011-12-10) This paper presents a dual reciprocity boundary element method (DRBEM) formulation coupled with an implicit backward difference time integration scheme for the solution of the incompressible magnetohydrodynamic (MHD) flow equations. The governing equations are the coupled system of Navier-Stokes equations and Maxwell's equations of electromagnetics through Ohm's law. We are concerned with a stream function-vorticity-magnetic induction-current density formulation of the full MHD equations in 2D. The stream f...
Efficient hybrid discrete Fourier transform-moment method for fast analysis of large rectangular arrays Chou, HT; Ho, HK; Pathak, PH; Nepa, P; Aydın Çivi, Hatice Özlem (Institution of Engineering and Technology (IET), 2002-02-01) A novel approach combining the moment method (MoM) and the discrete Fourier transform (DFT) is developed for the fast analysis of electromagnetic (EM) radiation/scattering from electrically large, finite, planar rectangular arrays. In particular, the unknown array distribution to be solved is represented in terms of the DFT within the MoM for a given array excitation. The proposed DFT-MoM approach for large arrays has the advantage that it can overcome the inefficiency of the conventional MoM approach by dr...
An improvement on the bounds of Weil exponential sums over Gallois rings with some applications Ling, S; Özbudak, Ferruh (Institute of Electrical and Electronics Engineers (IEEE), 2004-10-01) We present an upper bound for Weil-type exponential sums over Galois rings of characteristic p(2) which improves on the analog of the Weil-Carlitz-Uchiyama bound for Galois rings obtained by Kumar, Helleseth, and Calderbank. A more refined bound, expressed in terms of genera of function fields, and an analog of McEliece's theorem on the divisibility of the homogeneous weights of codewords in trace codes over Z(p)2, are also derived. These results lead to an improvement on the estimation of the minimum dista...

Citation Formats

B. Nakiboğlu, “The Sphere Packing Bound for Memoryless Channels,” PROBLEMS OF INFORMATION TRANSMISSION, pp. 201–244, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63192.