Evaluation of the Union Bound Using Characteristic Functions for Coded Transmission over Memoryless Channels

2021 ◽  
Author(s):  
A. N. Trofimov ◽  
F. A. Taubin
Keyword(s):  
Characteristic Functions ◽  
Memoryless Channels ◽  
Union Bound

scholarly journals Evaluation of the union bound for the decoding error probability using characteristic functions

2021 ◽  
pp. 71-85
Author(s):  
Andrey Trofimov ◽  
Feliks Taubin
Keyword(s):  
Numerical Integration ◽  
Wide Class ◽  
Error Probability ◽  
Integral Form ◽  
Characteristic Functions ◽  
Maximum Likelihood Decoding ◽  
Coding Schemes ◽  
Memoryless Channels ◽  
Union Bound ◽  
Final Expression

Introduction: Since the exact value of a decoding error probability cannot usually be calculated, an upper bounding technique is used. The standard approach for obtaining the upper bound on the maximum likelihood decoding error probability is based on the use of the union bound and the Chernoff bound, as well as its modifications. For many situations, this approach is not accurate enough. Purpose: Development of a method for exact calculation of the union bound for a decoding error probability, for a wide class of codes and memoryless channels. Methods: Use of characteristic functions of logarithm of the likelihood ratio for an arbitrary pair of codewords, trellis representation of codes and numerical integration. Results: The resulting exact union bound on the decoding error probability is based on a combination of the use of characteristic functions and the product of trellis diagrams for the code, which allows to obtain the final expression in an integral form convenient for numerical integration. An important feature of the proposed procedure is that it allows one to accurately calculate the union bound using an approach based on the use of transfer (generating) functions. With this approach, the edge labels in the product of trellis diagrams for the code are replaced by their corresponding characteristic functions. The final expression allows, using the standard methods of numerical integration, to calculate the values of the union bound on the decoding error probability with the required accuracy. Practical relevance: The results presented in this article make it possible to significantly improve the accuracy of the bound of the error decoding probability, and thereby increase the efficiency of technical solutions in the design of specific coding schemes for a wide class of communication channels.

scholarly journals Micro-CT and Microscopy Study of Internal and Marginal Gap to Tooth Surface of Crenelated versus Conventional Dental Indirect Veneers

Medicina ◽  
2021 ◽  
Vol 57 (8) ◽  
pp. 772
Author(s):  
Alexandra-Cristina Măroiu ◽  
Cosmin Sinescu ◽  
Virgil-Florin Duma ◽  
Florin Topală ◽  
Anca Jivănescu ◽  
...  
Keyword(s):  
Computer Aided Design ◽  
Tooth Surface ◽  
Characteristic Functions ◽  
The Novel ◽  
Micro Ct ◽  
Marginal Gap ◽  
Luting Cement ◽  
Computer Aided ◽  
Internal Adaptation ◽  
Internal Gap

1. Background and Objectives: Ceramic veneers represent the most appropriate treatment option for minimally invasive aesthetic rehabilitation. For long-term clinical success, the accurate marginal and internal adaptation of dental restorations are of paramount importance. The aim of this in vitro study is to assess the effect of a novel (patented) design of veneers compared to conventional ones on their marginal and internal gap to the prepared tooth surface. 2. Materials and Methods: Twenty-four lithium disilicate ceramic veneers are obtained using Computer-Aided-Design (CAD) and then milled using Computer-Aided-Manufacturing (CAM). The samples are divided into two groups: 12 conventional (CO) veneers (i.e., with a linear marginal contour) and 12 crenelated (CR) veneers, the latter with the novel sinusoidal marginal design. All samples are bonded to frontal teeth, and the adhesive interfaces are analyzed using two methods, optical microscopy and micro-Computed Tomography (CT): the former for the accuracy of the marginal gap and the latter for the internal gap (as well as for the homogeneity of the luting cement) of ceramic veneers. 3. Results: STATA and one-way ANOVA tests reveal significant differences between CO and CR veneers: (i) the marginal gap is smaller for CR (64 μm) than for CO veneers (236 μm); (ii) the internal adaptation is better for CR veneers: for a cement width of up to 120 μm, the covered surface for the CR group is 81.5%, while for the CO group it is 64.5%; (iii) the mean of the porosities within the cement is not significantly different (3.4 × 106 μm3 for CO and 3.9 × 106 μm3 for CR veneers), with a higher standard deviation for the CO group. Analytical modeling is achieved for internal gaps using the micro-CT results. The characteristic functions obtained allow us to compare the volume of luting cement for the two types of veneers. 4. Conclusion: The novel veneers design produces an improvement in the marginal and internal adaptation of the restorations to the prepared tooth surface. Thus, it provides favorable premises for better clinical performances.

scholarly journals The Role of Neuropeptide Y in the Nucleus Accumbens

2021 ◽  
Vol 22 (14) ◽  
pp. 7287
Author(s):  
Masaki Tanaka ◽  
Shunji Yamada ◽  
Yoshihisa Watanabe
Keyword(s):  
Nervous System ◽  
Nucleus Accumbens ◽  
Neuropeptide Y ◽  
Emotional Behavior ◽  
Characteristic Functions ◽  
Receptor Subtypes ◽  
Neuroendocrine Mechanisms ◽  
Fear And Anxiety ◽  
The Brain

Neuropeptide Y (NPY), an abundant peptide in the central nervous system, is expressed in neurons of various regions throughout the brain. The physiological and behavioral effects of NPY are mainly mediated through Y1, Y2, and Y5 receptor subtypes, which are expressed in regions regulating food intake, fear and anxiety, learning and memory, depression, and posttraumatic stress. In particular, the nucleus accumbens (NAc) has one of the highest NPY concentrations in the brain. In this review, we summarize the role of NPY in the NAc. NPY is expressed principally in medium-sized aspiny neurons, and numerous NPY immunoreactive fibers are observed in the NAc. Alterations in NPY expression under certain conditions through intra-NAc injections of NPY or receptor agonists/antagonists revealed NPY to be involved in the characteristic functions of the NAc, such as alcohol intake and drug addiction. In addition, control of mesolimbic dopaminergic release via NPY receptors may take part in these functions. NPY in the NAc also participates in fat intake and emotional behavior. Accumbal NPY neurons and fibers may exert physiological and pathophysiological actions partly through neuroendocrine mechanisms and the autonomic nervous system.

PRICING VARIANCE SWAPS UNDER DOUBLE HESTON STOCHASTIC VOLATILITY MODEL WITH STOCHASTIC INTEREST RATE

2021 ◽  
pp. 1-17
Author(s):  
Huojun Wu ◽  
Zhaoli Jia ◽  
Shuquan Yang ◽  
Ce Liu
Keyword(s):  
Interest Rate ◽  
Closed Form ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Characteristic Functions ◽  
Stochastic Interest Rate ◽  
Modeling Framework ◽  
Variance Swaps ◽  
Volatility Model ◽  
Stochastic Interest

In this paper, we discuss the problem of pricing discretely sampled variance swaps under a hybrid stochastic model. Our modeling framework is a combination with a double Heston stochastic volatility model and a Cox–Ingersoll–Ross stochastic interest rate process. Due to the application of the T-forward measure with the stochastic interest process, we can only obtain an efficient semi-closed form of pricing formula for variance swaps instead of a closed-form solution based on the derivation of characteristic functions. The practicality of this hybrid model is demonstrated by numerical simulations.

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