The Sphere Packing Bound via Augustin's Method

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 result continues to hold under a milder stationarity hypothesis.


The Sphere Packing Bound for Memoryless Channels
Nakiboğlu, Barış (Pleiades Publishing Ltd, 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 te...
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...
The Renyi Capacity and Center
Nakiboğlu, Barış (Institute of Electrical and Electronics Engineers (IEEE), 2019-02-01)
Renyi's information measures-the Renyi information, mean, capacity, radius, and center-are analyzed relying on the elementary properties of the Renyi divergence and the power means. The van Erven-Harremoes conjecture is proved for any positive order and for any set of probability measures on a given measurable space and a generalization of it is established for the constrained variant of the problem. The finiteness of the order alpha Renyi capacity is shown to imply the continuity of the Renyi capacity on (...
Sampling of the Wiener Process for Remote Estimation Over a Channel With Random Delay
Sun, Yin; Polyanskiy, Yury; Uysal, Elif (Institute of Electrical and Electronics Engineers (IEEE), 2020-02-01)
In this paper, we consider a problem of sampling a Wiener process, with samples forwarded to a remote estimator over a channel that is modeled as a queue. The estimator reconstructs an estimate of the real-time signal value from causally received samples. We study the optimal online sampling strategy that minimizes the mean square estimation error subject to a sampling rate constraint. We prove that the optimal sampling strategy is a threshold policy, and find the optimal threshold. This threshold is determ...
On Linear Complementary Pairs of Codes
CARLET, Claude; Guneri, Cem; Özbudak, Ferruh; Ozkaya, Buket; SOLE, Patrick (Institute of Electrical and Electronics Engineers (IEEE), 2018-10-01)
We study linear complementary pairs (LCP) of codes (C, D), where both codes belong to the same algebraic code family. We especially investigate constacyclic and quasicyclic LCP of codes. We obtain characterizations for LCP of constacyclic codes and LCP of quasi-cyclic codes. Our result for the constacyclic complementary pairs extends the characterization of linear complementary dual (LCD) cyclic codes given by Yang and Massey. We observe that when C and I) are complementary and constacyclic, the codes C and...
Citation Formats
B. Nakiboğlu, “The Sphere Packing Bound via Augustin’s Method,” IEEE TRANSACTIONS ON INFORMATION THEORY, pp. 816–840, 2019, Accessed: 00, 2020. [Online]. Available: