The Augustin center and the sphere packing bound for memoryless channels

For any channel with a convex constraint set and finite Augustin capacity, existence of a unique Augustin center and associated Erven-llarremoes bound are established. Augustin-Legendre capacity, center, and radius are introduced and proved to be equal to the corresponding Renyi-Gallager entities. Sphere packing bounds with polynomial prefactors are derived for codes on two families of channels: (possibly non-stationary) memoryless channels with multiple additive cost constraints and stationary memoryless channels with convex constraints on the empirical distribution of the input codewords.


A Simple Derivation of the Refined SPB for the Constant Composition Codes
Nakiboğlu, Barış (2019-07-01)
A judicious application of the Berry-Esseen theorem via the concepts of Augustin information and mean is demonstrated to be sufficient for deriving the sphere packing bound with a prefactor that is Omega(n(-0.5(1-E'sp(R,W,p)))) for the constant composition codes. The resulting non-asymptotic bounds have definite approximation error terms.
The Calabi (Veronese) imbeddings as integral submanifolds of CP2n+1
Blair, DE; Korkmaz, Belgin; Vrancken, L (2000-05-01)
Considering odd-dimensional complex projective space as a complex contact manifold, one may ask which of the Calabi (Veronese) imbeddings can be positioned by a holomorphic congruence as integral submanifolds of the complex contact structure. It is first shown that when the first normal space is the whole normal space, this is impossible. It is also shown to be impossibile for a Calabi surface (complex dimension 2) in complex projective space of dimension 9 where one has both a first and second normal space...
The property of smallness up to a complemented Banach subspace
Abdeljawad, T; Yurdakul, Murat Hayrettin (2004-04-01)
This article investigates locally convex spaces which satisfy the property of smallness up to a complemented Banach subspace, the SCBS property, which was introduced by Djakov, Terzioglu, Yurdakul and Zahariuta. It is proved that a bounded perturbation of an automorphism on a complete barrelled locally convex, space with the SCBS is stable up to a Banach subspace. New examples are given, and the relation of the SCBS with the quasinormability is analyzed. It is proved that the Frechet space l(p+) does not sa...
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...
The path integral quantization and the construction of the S-matrix operator in the Abelian and non-Abelian Chern-Simons theories
Fainberg, VY; Pak, Namık Kemal; Shikakhwa, MS (IOP Publishing, 1997-06-07)
The covariant path integral quantization of the theory of the scalar and spinor fields interacting through the Abelian and non-Abelian Chern-Simons gauge fields in 2 + 1 dimensions is carried out using the De Witt-Fadeev-Popov method. The mathematical ill-definiteness of the path integral of theories with pure Chern-Simons' fields is remedied by the introduction of the Maxwell or Maxwell-type (in the non-Abelian case) terms, which make the resulting theories super-renormalizable and guarantees their gauge-i...
Citation Formats
B. Nakiboğlu, “The Augustin center and the sphere packing bound for memoryless channels,” 2017, Accessed: 00, 2020. [Online]. Available: