Factorization of Joint Probability Mass Functions into Parity Check Interactions

Bayramoglu, Muhammet Fatih
Yılmaz, Ali Özgür
We show that any joint probability mass function (PMF) can be expressed as a product of parity check factors an d factors of degree one with the help of some auxiliary variables, if the alphabet size is appropriate for defining a parity chec k equation. In other words, marginalization of a joint PMF is equivalent to a soft decoding task as long as a finite field can be constructed over the alphabet of the PMF. In factor graph terminology this claim means that a factor graph representing such a joint PMF always has an equivalent Tanner graph. We provide a systematic method based on the Hilbert space of PMF s and orthogonal projections for obtaining this factorization.


Factorization of some polynomials over finite local commutative rings and applications to certain self-dual and LCD codes
Koese, Seyda; Özbudak, Ferruh (2022-03-01)
We determine the unique factorization of some polynomials over a finite local commutative ring with identity explicitly. This solves and generalizes the main conjecture of Qian, Shi and Sole in [13]. We also give some applications to enumeration of certain generalized double circulant self-dual and linear complementary dual (LCD) codes over some finite rings together with an application in asymptotic coding theory.
Factorization of unbounded operators on Kothe spaces
Terzioglou, T; Yurdakul, Murat Hayrettin; Zuhariuta, V (2004-01-01)
The main result is that the existence of an unbounded continuous linear operator T between Kothe spaces lambda(A) and lambda(C) which factors through a third Kothe space A(B) causes the existence of an unbounded continuous quasidiagonal operator from lambda(A) into lambda(C) factoring through lambda(B) as a product of two continuous quasidiagonal operators. This fact is a factorized analogue of the Dragilev theorem [3, 6, 7, 2] about the quasidiagonal characterization of the relation (lambda(A), lambda(B)) ...
Tensor form factors of the octet hyperons in QCD
Küçükarslan, Ayşe; Özdem, Ulaş; Özpineci, Altuğ (American Physical Society (APS), 2016-11-11)
Light-cone QCD sum rules to leading order in QCD are used to investigate the tensor form factors of the Sigma-Sigma,Xi-Xi, and Sigma-Lambda transitions in the range 1 GeV2 <= Q(2) <= 10 GeV2. The DAs of Sigma,Xi, and. baryon have been calculated without higher-order terms. Then, studies including higher-order corrections have been done for the Sigma and. baryon Lambda The resulting form factors are obtained using these two DAs. We make a comparison with the predictions of the chiral quark soliton model.
Excessive backlog probabilities of two parallel queues
Unlu, Kamil Demirberk; Sezer, Ali Devin (2020-10-01)
Let X be the constrained random walk on Z2 + with increments (1, 0), (-1, 0), (0, 1) and (0,-1); X represents, at arrivals and service completions, the lengths of two queues (or two stacks in computer science applications) working in parallel whose service and interarrival times are exponentially distributed with arrival rates.i and service rates mu i, i = 1, 2; we assume.i < mu i, i = 1, 2, i.e., X is assumed stable. Without loss of generality we assume.1 =.1/mu 1 similar to.2 =.2/mu 2. Let tn be the first...
Improved Three-Way Split Formulas for Binary Polynomial and Toeplitz Matrix Vector Products
Cenk, Murat; Hasan, M. Anwar (2013-07-01)
In this paper, we consider three-way split formulas for binary polynomial multiplication and Toeplitz matrix vector product (TMVP). We first recall the best known three-way split formulas for polynomial multiplication: the formulas with six recursive multiplications given by Sunar in a 2006 IEEE Transactions on Computers paper and the formula with five recursive multiplications proposed by Bernstein at CRYPTO 2009. Second, we propose a new set of three-way split formulas for polynomial multiplication that a...
Citation Formats
M. F. Bayramoglu and A. Ö. Yılmaz, “Factorization of Joint Probability Mass Functions into Parity Check Interactions,” 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36636.