The Sphere Packing Bound for Memoryless Channels

2020-07-01
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.
PROBLEMS OF INFORMATION TRANSMISSION

Suggestions

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 Greedy Link Scheduler for Wireless Networks With Gaussian Multiple-Access and Broadcast Channels
Sridharan, Arun; Koksal, C. Emre; Uysal, Elif (Institute of Electrical and Electronics Engineers (IEEE), 2012-02-01)
Information-theoretic broadcast channels (BCs) and multiple-access channels (MACs) enable a single node to transmit data simultaneously to multiple nodes, and multiple nodes to transmit data simultaneously to a single node, respectively. In this paper, we address the problem of link scheduling in multihop wireless networks containing nodes with BC and MAC capabilities. We first propose an interference model that extends protocol interference models, originally designed for point-to-point channels, to includ...
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...
The Augustin Capacity and Center
Nakiboğlu, Barış (Pleiades Publishing Ltd, 2019-10-01)
For any channel, the existence of a unique Augustin mean is established for any positive order and probability mass function on the input set. The Augustin mean is shown to be the unique fixed point of an operator defined in terms of the order and the input distribution. The Augustin information is shown to be continuously differentiable in the order. For any channel and convex constraint set with finite Augustin capacity, the existence of a unique Augustin center and the associated van Erven-Harremoes boun...
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...
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.