Degrees of Freedom of a Communication Channel and Kolmogorov numbers
نویسندگان
چکیده
In this note, we show that the operator theoretic concept of Kolmogorov numbers and the number of degrees of freedom at level ǫ of a communication channel are closely related. Linear communication channels may be modeled using linear compact operators on Banach or Hilbert spaces and the number of degrees of freedom of such channels is defined to be the number of linearly independent signals that may be communicated over this channel, where the channel is restricted by a threshold noise level. Kolmogorov numbers are a particular example of s-numbers, which are defined over the class of bounded operators between Banach spaces. We demonstrate that these two concepts are closely related, namely that the Kolmogorov numbers correspond to the “jump points” in the function relating numbers of degrees of freedom with the noise level ǫ. We also establish a useful numerical computation result for evaluating Kolmogorov numbers of compact operators.
منابع مشابه
On the natural stabilization of convection diffusion problems using LPIM meshless method
By using the finite element $p$-Version in convection-diffusion problems, we can attain to a stabilized and accurate results. Furthermore, the fundamental of the finite element $p$-Version is augmentation degrees of freedom. Based on the fact that the finite element and the meshless methods have similar concept, it is obvious that many ideas in the finite element can be easily used in the meshl...
متن کاملThe Kinematic Analysis Of Four Degrees Of Freedom For A Medical Robot And Control It By Labview And Arduino Mega2560 (Simulation And Implementation)
ABSRACTThis study presents the kinematic analysis of a four-degree freedom medical robotic arm using the Matlab and the robotic-tool, the arm was designed using a solid work program, As well as details of the control of the real design of this arm using Arduino Mega 2560, The specialist enters the position to be reached by the automatic arm (injection position), Or moving the arm to any p...
متن کاملAn Efficient Strain Based Cylindrical Shell Finite Element
The need for compatibility between degrees of freedom of various elements is a major problem encountered in practice during the modeling of complex structures; the problem is generally solved by an additional rotational degree of freedom [1-3]. This present paper investigates possible improvements to the performances of strain based cylindrical shell finite element [4] by introducing an additio...
متن کاملDegrees of Freedom of a Communication Channel: Using Generalised Singular Values
A fundamental problem in any communication system is: given a communication channel between a transmitter and a receiver, how many “independent” signals can be exchanged between them? Arbitrary communication channels that can be described by linear compact channel operators mapping between normed spaces are examined in this paper. The (well-known) notions of degrees of freedom at level ǫ and es...
متن کاملInterference Alignment and the Degrees of Freedom for the 3 User Interference Channel
We explore the degrees of freedom region for the 3 user wireless interference channel with perfect channel knowledge at all nodes. While the best known outerbound for the K user interference channel states that there cannot be more than K/2 degrees of freedom, it has been conjectured that in general the constant interference channel with any number of users has only one degree of freedom. We sh...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1103.3510 شماره
صفحات -
تاریخ انتشار 2011