A Hilbert Space of Probability Mass Functions and Applications on the Sum-Product Algorithm

Bayramoglu, Muhammet Fatih
Yılmaz, Ali Özgür
In this paper a Hilbert space structure of probability mass functions (PMF) will be presented. The tools provided by the Hilbert space, specifically the norm and the inner product, may be useful while analyzing and improving the sum-product algorithm in many aspects. Our approach provides a metric distance between PMFs and a new point of a view of the log-likelihood ratio (LLR) such that the LLR representation is nothing but a Hilbert space representation.
5th International Symposium on Turbo Codes and Related Topics


The Hilbert Space of probability mass functions and applications on probabilistic Inference
Bayramoğlu, Muhammet Fatih; Yılmaz, Ali Özgür; Department of Electrical and Electronics Engineering (2011)
The Hilbert space of probability mass functions (pmf) is introduced in this thesis. A factorization method for multivariate pmfs is proposed by using the tools provided by the Hilbert space of pmfs. The resulting factorization is special for two reasons. First, it reveals the algebraic relations between the involved random variables. Second, it determines the conditional independence relations between the random variables. Due to the first property of the resulting factorization, it can be shown that channe...
BASKAL, S; ERIS, A; SATIR, A (1994-12-19)
The symmetries and associated conservation laws of the SO(2,1) invariant non-linear sigma model equations in 1+1 dimensions are investigated. An infinite family of generalized local symmetries is presented and the uniqueness of these solutions is discussed.
A New Representation of Elements of Binary Fields with Subquadratic Space Complexity Multiplication of Polynomials
Özbudak, Ferruh; Cenk, Murat (2013-10-01)
In this paper, Hermite polynomial representation is proposed as an alternative way to represent finite fields of characteristic two. We show that multiplication in Hermite polynomial representation can be achieved with subquadratic space complexity. This representation enables us to find binomial or trinomial irreducible polynomials which allows us faster modular reduction over binary fields when there is no desirable such low weight irreducible polynomial in other representations. We then show that the pro...
A note on the importance of mass conservation in long-time stability of Navier-Stokes simulations using finite elements
Belenli, Mine Akbas; Rebholz, Leo G.; Tone, Florentina (2015-07-01)
We prove a long-time stability result for the finite element in space, linear extrapolated Crank-Nicolson in time discretization of the Navier-Stokes equations (NSE). From this result and a numerical experiment, we show the importance of discrete mass conservation in long-time simulations of the NSE. That is, we show that using elements that strongly enforce mass conservation can provide significantly more accurate solutions over long times, compared to those that enforce it weakly.
An Application of the rayleigh-ritz method to the integral-equation representation of the one-dimensional schrödinger equation
Kaya, Ruşen; Taşeli, Hasan; Department of Mathematics (2019)
In this thesis, the theory of the relations between differential and integral equations is analyzed and is illustrated by the reformulation of the one-dimensional Schrödinger equation in terms of an integral equation employing the Green’s function. The Rayleigh- Ritz method is applied to the integral-equation formulation of the one-dimensional Schrödinger equation in order to approximate the eigenvalues of the corresponding singular problem within the desired accuracy. The outcomes are compared with those r...
Citation Formats
M. F. Bayramoglu and A. Ö. Yılmaz, “A Hilbert Space of Probability Mass Functions and Applications on the Sum-Product Algorithm,” presented at the 5th International Symposium on Turbo Codes and Related Topics, Lausanne, SWITZERLAND, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39906.