scholarly journals Closed Form Aliasing Probability For Q-ary Symmetric Errors

VLSI Design ◽  
1996 ◽  
Vol 4 (3) ◽  
pp. 199-205
Author(s):  
Geetani Edirisooriya
Keyword(s):  
Closed Form ◽  
Circuit Complexity ◽  
Propagation Delay ◽  
Linear Feedback ◽  
Closed Form Expression ◽  
Primitive Polynomials ◽  
Test Circuit ◽  
Signature Analyzer ◽  
Multiple Input ◽  
Aliasing Probability

In Built-In Self-Test (BIST) techniques, test data reduction can be achieved using Linear Feedback Shift Registers (LFSRs). A faulty circuit may escape detection due to loss of information inherent to data compaction schemes. This is referred to as aliasing. The probability of aliasing in Multiple-Input Shift-Registers (MISRs) has been studied under various bit error models. By modeling the signature analyzer as a Markov process we show that the closed form expression derived for aliasing probability previously, for MISRs with primitive polynomials under q-ary symmetric error model holds for all MISRs irrespective of their feedback polynomials and for group cellular automata signature analyzers as well. If the erroneous behaviour of a circuit can be modelled with q-ary symmetric errors, then the test circuit complexity and propagation delay associated with the signature analyzer can be minimized by using a set of m single bit LFSRs without increasing the probability of aliasing.

Aliasing probability for multiple input signature analyzer

1990 ◽  
Vol 39 (4) ◽  
pp. 586-591 ◽  
Author(s):  
D.K. Pradhan ◽  
S.K. Gupta ◽  
M.G. Karpovsky
Keyword(s):  
Signature Analyzer ◽  
Multiple Input ◽  
Aliasing Probability

scholarly journals Bit error rate performance analysis of AC-MAP in multiple input single output wireless relay network

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Taha A. Khalaf ◽  
Hazem Mohammed
Keyword(s):  
Closed Form ◽  
Bit Error Rate ◽  
Error Rate ◽  
Relay Network ◽  
Closed Form Expression ◽  
Channel Noise ◽  
Single Output ◽  
Multiple Input ◽  
End To End ◽  
Map Decoder

AbstractIn this paper, we propose a joint decoding scheme called AC-MAP decoder for multiple input single output (MISO) wireless cooperative communication network that consists of single source, single relay, and single destination. The proposed scheme is based on both Alamouti combining (AC) scheme and maximum a posteriori (MAP) decoder and is used to estimate the data at the destination. The AC-MAP decoder is optimal in the sense that it minimizes the end-to-end bit error rate (BER). In order to analyze performance of the proposed decoder, we derive a closed form expression for the upper bound (UB) on the end-to-end error probability. Distances between system nodes, transmit energy, and channel noise and fading effects are considered in the derivation of the UB. Numerical results show that the closed form UB is very tight and it almost coincides with the exact BER results obtained from simulations. Therefore, we use the derived UB expression to study the effects of the relay position on the BER performance and to find the optimal location of the relay node.

scholarly journals Synthesizing of Planar and Conformal Double-Sided Parallel-Cross Dipoles FSS Based on Closed-Form Expression

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Yassine Zouaoui ◽  
Larbi Talbi ◽  
Khelifa Hettak ◽  
Naresh K. Darimireddy
Keyword(s):  
Closed Form ◽  
Closed Form Expression ◽  
Form Expression

Distribution of Consensus in a Broadcasting-based Consensus-forming Algorithm

2021 ◽  
Vol 48 (3) ◽  
pp. 91-96
Author(s):  
Shigeo Shioda
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Closed Form ◽  
Probability Density ◽  
Infinite Number ◽  
Stable Distribution ◽  
Random Variable ◽  
Cauchy Distribution ◽  
Closed Form Expression ◽  
Form Expression

The consensus achieved in the consensus-forming algorithm is not generally a constant but rather a random variable, even if the initial opinions are the same. In the present paper, we investigate the statistical properties of the consensus in a broadcasting-based consensus-forming algorithm. We focus on two extreme cases: consensus forming by two agents and consensus forming by an infinite number of agents. In the two-agent case, we derive several properties of the distribution function of the consensus. In the infinite-numberof- agents case, we show that if the initial opinions follow a stable distribution, then the consensus also follows a stable distribution. In addition, we derive a closed-form expression of the probability density function of the consensus when the initial opinions follow a Gaussian distribution, a Cauchy distribution, or a L´evy distribution.

scholarly journals Colored HOMFLY-PT for hybrid weaving knot $$ {\hat{\mathrm{W}}}_3 $$(m, n)

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Vivek Kumar Singh ◽  
Rama Mishra ◽  
P. Ramadevi
Keyword(s):  
Closed Form ◽  
Topological Strings ◽  
Chebyshev Polynomials ◽  
Fibonacci Numbers ◽  
Infinite Family ◽  
Closed Form Expression ◽  
Two Dimensional ◽  
Laurent Polynomials ◽  
Form Expression ◽  
Torus Knots

Abstract Weaving knots W(p, n) of type (p, n) denote an infinite family of hyperbolic knots which have not been addressed by the knot theorists as yet. Unlike the well known (p, n) torus knots, we do not have a closed-form expression for HOMFLY-PT and the colored HOMFLY-PT for W(p, n). In this paper, we confine to a hybrid generalization of W(3, n) which we denote as $$ {\hat{W}}_3 $$ W ̂ 3 (m, n) and obtain closed form expression for HOMFLY-PT using the Reshitikhin and Turaev method involving $$ \mathrm{\mathcal{R}} $$ ℛ -matrices. Further, we also compute [r]-colored HOMFLY-PT for W(3, n). Surprisingly, we observe that trace of the product of two dimensional $$ \hat{\mathrm{\mathcal{R}}} $$ ℛ ̂ -matrices can be written in terms of infinite family of Laurent polynomials $$ {\mathcal{V}}_{n,t}\left[q\right] $$ V n , t q whose absolute coefficients has interesting relation to the Fibonacci numbers $$ {\mathrm{\mathcal{F}}}_n $$ ℱ n . We also computed reformulated invariants and the BPS integers in the context of topological strings. From our analysis, we propose that certain refined BPS integers for weaving knot W(3, n) can be explicitly derived from the coefficients of Chebyshev polynomials of first kind.

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