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İbrahim Çanak - One of the best experts on this subject based on the ideXlab platform.

  • Some conditions under which slow oscillation of a Sequence of fuzzy numbers follows from Ces`{a}ro summability of its Generator Sequence
    Iranian Journal of Fuzzy Systems, 2014
    Co-Authors: İbrahim Çanak
    Abstract:

    Let $(u_n)$ be a Sequence of fuzzy numbers.  We recover the slow oscillation of $(u_n)$ of fuzzy numbers from the Ces`{a}ro summability of its Generator Sequence and some additional conditions imposed on $(u_n)$. Further, fuzzy analogues of some well known classical Tauberian theorems for Ces`{a}ro summability method are established as particular cases.

  • extended tauberian theorem for the weighted mean method of summability
    Ukrainian Mathematical Journal, 2013
    Co-Authors: İbrahim Çanak, Ümit Totur
    Abstract:

    We prove a new Tauberian-like theorem. For a real Sequence u = (u n ), on the basis of the weighted mean summability of its Generator Sequence (V (0) n,p (∆u)) and some other conditions, this theorem establishes the property of slow oscillation of the indicated Sequence.

  • On the (C,1) summability method of improper integrals
    Applied Mathematics and Computation, 2013
    Co-Authors: Imit Totur, İbrahim Çanak
    Abstract:

    In this paper we prove a Tauberian-like theorem to retrieve the slow oscillation of a real-valued function s(x) from its (C,1) summability of the Generator Sequence v(x) and one-sidedly boundedness of the general control modulo of integer order m>=1 with respect to a function satisfying an appropriate condition.

  • Some Tauberian conditions for Cesàro summability method
    Mathematica Slovaca, 2012
    Co-Authors: İbrahim Çanak, Ümit Totur
    Abstract:

    Let u = ( u _ n ) be a Sequence of real numbers whose Generator Sequence is Cesàro summable to a finite number. We prove that ( u _ n ) is slowly oscillating if the Sequence of Cesàro means of ( ω _ n ^( m −1) ( u )) is increasing and the following two conditions are hold: $$\begin{gathered} \left( {\lambda - 1} \right)\mathop {\lim \sup }\limits_n \left( {\frac{1} {{\left[ {\lambda n} \right] - n}}\sum\limits_{k = n + 1}^{\left[ {\lambda n} \right]} {\left( {\omega _k^{\left( m \right)} \left( u \right)} \right)^q } } \right)^{\frac{1} {q}} = o\left( 1 \right), \lambda \to 1^ + , q > 1, \hfill \\ \left( {1 - \lambda } \right)\mathop {\lim \sup }\limits_n \left( {\frac{1} {{n - \left[ {\lambda n} \right]}}\sum\limits_{k = \left[ {\lambda n} \right] + 1}^n {\left( {\omega _k^{\left( m \right)} \left( u \right)} \right)^q } } \right)^{\frac{1} {q}} = o\left( 1 \right), \lambda \to 1^ - , q > 1, \hfill \\ \end{gathered}$$ where ( ω _ n ^( m ) ( u )) is the general control modulo of the oscillatory behavior of integer order m ≥ 1 of a Sequence ( u _ n ) defined in [DİK, F.: Tauberian theorems for convergence and subsequential convergence with moderately oscillatory behavior , Math. Morav. 5 , (2001), 19–56] and [ λn ] denotes the integer part of λn .

  • some tauberian theorems for the weighted mean methods of summability
    Computers & Mathematics With Applications, 2011
    Co-Authors: İbrahim Çanak, Imit Totur
    Abstract:

    In this paper, we introduce the concept of the weighted Generator Sequence and prove that certain conditions in terms of weighted Generator Sequences are Tauberian conditions for the weighted mean summability method.

B.s. Rajan - One of the best experts on this subject based on the ideXlab platform.

  • An efficient algorithm for constructing minimal trellises for codes over finite abelian groups
    IEEE Transactions on Information Theory, 1996
    Co-Authors: Vijay V. Vazirani, Huzur Saran, B.s. Rajan
    Abstract:

    We present an efficient algorithm for computing the minimal trellis for a group code over a finite abelian group, given a Generator matrix for the code. We also show how to compute a succinct representation of the minimal trellis for such a code, and present algorithms that use this information to compute efficiently local descriptions of the minimal trellis. This extends the work of Kschischang and Sorokine (see ibid., vol.41, no.6, p.1926-37, 1995), who treated the case of linear codes over fields. An important application of our algorithms is to the construction of minimal trellises for lattices. A key step in our work is handling codes over cyclic groups C/sub p//spl alpha/, where p is a prime. Such a code can be viewed as a module over the ring Z/sub p//spl alpha/. Because of the presence of zero divisors in the ring, modules do not share the useful properties of vector spaces. We get around this difficulty by restricting the notion of linear combination to a p-linear combination, and by introducing the notion of a p-Generator Sequence, which enjoys properties similar to those of a Generator matrix for a vector space.

  • FOCS - An efficient algorithm for constructing minimal trellises for codes over finite Abelian groups
    Proceedings of 37th Conference on Foundations of Computer Science, 1
    Co-Authors: Vijay V. Vazirani, Huzur Saran, B.s. Rajan
    Abstract:

    We present an efficient algorithm for computing the minimal trellis for a group code over a finite Abelian group, given a Generator matrix for the code. We also show how to compute a succinct representation of the minimal trellis for such a code, and present algorithms that use this information to efficiently compute local descriptions of the minimal trellis. This extends the work of Kschischang and Sorokine (1995), who handled the case of linear codes over fields. An important application of our algorithms is to the construction of minimal trellises for lattices. A key step in our work is handling codes over cyclic groups C/sub p//spl alpha/, where p is a prime. Such a code can be viewed as a submodule over the ring Z/sub p//spl alpha/. Because of the presence of zero-divisors in the ring, submodules do not share the useful properties of vector spaces. We get around this difficulty by restricting the notion of linear combination to p-linear combination, and introducing the notion of a p-Generator Sequence, which enjoys properties similar to that of a Generator matrix for a vector space.

Vijay V. Vazirani - One of the best experts on this subject based on the ideXlab platform.

  • An efficient algorithm for constructing minimal trellises for codes over finite abelian groups
    IEEE Transactions on Information Theory, 1996
    Co-Authors: Vijay V. Vazirani, Huzur Saran, B.s. Rajan
    Abstract:

    We present an efficient algorithm for computing the minimal trellis for a group code over a finite abelian group, given a Generator matrix for the code. We also show how to compute a succinct representation of the minimal trellis for such a code, and present algorithms that use this information to compute efficiently local descriptions of the minimal trellis. This extends the work of Kschischang and Sorokine (see ibid., vol.41, no.6, p.1926-37, 1995), who treated the case of linear codes over fields. An important application of our algorithms is to the construction of minimal trellises for lattices. A key step in our work is handling codes over cyclic groups C/sub p//spl alpha/, where p is a prime. Such a code can be viewed as a module over the ring Z/sub p//spl alpha/. Because of the presence of zero divisors in the ring, modules do not share the useful properties of vector spaces. We get around this difficulty by restricting the notion of linear combination to a p-linear combination, and by introducing the notion of a p-Generator Sequence, which enjoys properties similar to those of a Generator matrix for a vector space.

  • FOCS - An efficient algorithm for constructing minimal trellises for codes over finite Abelian groups
    Proceedings of 37th Conference on Foundations of Computer Science, 1
    Co-Authors: Vijay V. Vazirani, Huzur Saran, B.s. Rajan
    Abstract:

    We present an efficient algorithm for computing the minimal trellis for a group code over a finite Abelian group, given a Generator matrix for the code. We also show how to compute a succinct representation of the minimal trellis for such a code, and present algorithms that use this information to efficiently compute local descriptions of the minimal trellis. This extends the work of Kschischang and Sorokine (1995), who handled the case of linear codes over fields. An important application of our algorithms is to the construction of minimal trellises for lattices. A key step in our work is handling codes over cyclic groups C/sub p//spl alpha/, where p is a prime. Such a code can be viewed as a submodule over the ring Z/sub p//spl alpha/. Because of the presence of zero-divisors in the ring, submodules do not share the useful properties of vector spaces. We get around this difficulty by restricting the notion of linear combination to p-linear combination, and introducing the notion of a p-Generator Sequence, which enjoys properties similar to that of a Generator matrix for a vector space.

Sanjay Sharma - One of the best experts on this subject based on the ideXlab platform.

  • Adaptive Generator Sequence Selection in Multilevel Space–Time Trellis Codes
    Wireless Personal Communications, 2014
    Co-Authors: Dharmvir Jain, Sanjay Sharma
    Abstract:

    It has been shown that multilevel space–time trellis codes (MLSTTCs) designed by combining multilevel coding (MLC) with space–time trellis codes (STTCs) can provide improvement in diversity gain and coding gain of the STTCs. MLSTTCs assume perfect channel state information (CSI) at receiver and no knowledge of CSI at transmitter. Weighted multilevel space–time trellis codes (WMLSTTCs), designed by combining MLSTTCs and perfect CSI at transmitter are capable of providing improvement in coding gain of MLSTTCs. In this paper, we present improvement in performance of MLSTTCs by using channel feedback information from the receiver for adaptive selection of Generator Sequences. The selected Generator Sequences are used for encoding the component STTCs. The receiver compares current channel profile at receiver with a set of predetermined channel profiles, and sends an index of a predefined channel profile closest to the current channel profile to the transmitter. The transmitter selects a code set that matches best with the current channel profile at receiver using the index. The selected code set having different sets of Generator Sequences is used by STTC encoders to generate dynamic space–time trellis codes (DSTTCs). The DSTTCs act as component codes in multilevel coding for generating new codes henceforth referred to as multilevel dynamic space–time trellis codes (MLDSTTCs). Analysis and simulation results show that MLDSTTCs provide improvement in performance over MLSTTCs.

  • Adaptive Generator Sequence Selection in Multilevel Space-Time Trellis Codes
    Wireless Personal Communications, 2013
    Co-Authors: Dharmvir Jain, Sanjay Sharma
    Abstract:

    It has been shown that multilevel space–time trellis codes (MLSTTCs) designed by combining multilevel coding (MLC) with space–time trellis codes (STTCs) can provide improvement in diversity gain and coding gain of the STTCs. MLSTTCs assume perfect channel state information (CSI) at receiver and no knowledge of CSI at transmitter. Weighted multilevel space–time trellis codes (WMLSTTCs), designed by combining MLSTTCs and perfect CSI at transmitter are capable of providing improvement in coding gain of MLSTTCs. In this paper, we present improvement in performance of MLSTTCs by using channel feedback information from the receiver for adaptive selection of Generator Sequences. The selected Generator Sequences are used for encoding the component STTCs. The receiver compares current channel profile at receiver with a set of predetermined channel profiles, and sends an index of a predefined channel profile closest to the current channel profile to the transmitter. The transmitter selects a code set that matches best with the current channel profile at receiver using the index. The selected code set having different sets of Generator Sequences is used by STTC encoders to generate dynamic space–time trellis codes (DSTTCs). The DSTTCs act as component codes in multilevel coding for generating new codes henceforth referred to as multilevel dynamic space–time trellis codes (MLDSTTCs). Analysis and simulation results show that MLDSTTCs provide improvement in performance over MLSTTCs.

Huzur Saran - One of the best experts on this subject based on the ideXlab platform.

  • An efficient algorithm for constructing minimal trellises for codes over finite abelian groups
    IEEE Transactions on Information Theory, 1996
    Co-Authors: Vijay V. Vazirani, Huzur Saran, B.s. Rajan
    Abstract:

    We present an efficient algorithm for computing the minimal trellis for a group code over a finite abelian group, given a Generator matrix for the code. We also show how to compute a succinct representation of the minimal trellis for such a code, and present algorithms that use this information to compute efficiently local descriptions of the minimal trellis. This extends the work of Kschischang and Sorokine (see ibid., vol.41, no.6, p.1926-37, 1995), who treated the case of linear codes over fields. An important application of our algorithms is to the construction of minimal trellises for lattices. A key step in our work is handling codes over cyclic groups C/sub p//spl alpha/, where p is a prime. Such a code can be viewed as a module over the ring Z/sub p//spl alpha/. Because of the presence of zero divisors in the ring, modules do not share the useful properties of vector spaces. We get around this difficulty by restricting the notion of linear combination to a p-linear combination, and by introducing the notion of a p-Generator Sequence, which enjoys properties similar to those of a Generator matrix for a vector space.

  • FOCS - An efficient algorithm for constructing minimal trellises for codes over finite Abelian groups
    Proceedings of 37th Conference on Foundations of Computer Science, 1
    Co-Authors: Vijay V. Vazirani, Huzur Saran, B.s. Rajan
    Abstract:

    We present an efficient algorithm for computing the minimal trellis for a group code over a finite Abelian group, given a Generator matrix for the code. We also show how to compute a succinct representation of the minimal trellis for such a code, and present algorithms that use this information to efficiently compute local descriptions of the minimal trellis. This extends the work of Kschischang and Sorokine (1995), who handled the case of linear codes over fields. An important application of our algorithms is to the construction of minimal trellises for lattices. A key step in our work is handling codes over cyclic groups C/sub p//spl alpha/, where p is a prime. Such a code can be viewed as a submodule over the ring Z/sub p//spl alpha/. Because of the presence of zero-divisors in the ring, submodules do not share the useful properties of vector spaces. We get around this difficulty by restricting the notion of linear combination to p-linear combination, and introducing the notion of a p-Generator Sequence, which enjoys properties similar to that of a Generator matrix for a vector space.