Other Computational Technique for Estimation of Lower Bound on Capacity of Two-Dimensional Diamond-1 Constrained Channel

Computational technique for lower bound on Two-dimensional Diamond-1 constrained channel capacity is presented in this paper. It is basically an amalgamation of Matrix Fractal Grow Method (MFGM) and a new Matrix Fractal Reduction Method both applicable to state transition matrices of the corresponding constrained channels and Rayleigh Quotient Iteration method. Also other programming tricks are presented which improve its implementation. Estimation of lower bound values on the mentioned capacity is made using it. The results are in good alignment with known exact results, which is a verification of the new method. The method could be generalized for other constraints which are restricted only on one neighbor symbol in 2D constrained channel such as for example Square-1 and Hexagonal-1

REED SOLOMON CODES FOR RELIABLE COMMUNICATION IN INTERNET OF THINGS (IOT)

In the networking field, Internet of Things ( IOT, shortly) is the current state of the art in the nowadays Information of Technology era. The networking may be defined as external network or internal network. The backbone of the IOT is the internet connections. The IOT connects various objects together to the internet so that they can communicate and exchange billions of data and information among various devices and services. They may be remotely controlled from distant area. As IOT systems will be open and available everywhere, a number of security issue may arise. One issue that remains open in the IOT technology is security and privacy issues. Because of this security issue, the communications among many different devices powered by IOT could not be said as a reliable technology. Because of this, the security of the IOT systems can be enhanced by adding error correction scheme both in communication channel as well as the data store. By introducing the error correction scheme, the risks may be reduced to acceptable level and the security could be enhanced. A Reed-Solomon (RS) code is one of many error control coding schemes that firstly introduced by Reed and Solomon in 1960. This code has been used in various applications, such as CD-ROMs, space communications, DVD technology, digital TV and much more. Here, Reed-Solomon code is discussed in detail. It raised the issue of RS decoding scheme using the Welch Berlekamp algorithm. It presents the implementation of the Welch Berlekamp algorithm for RS decoder in detail. The VHDL implementation VHDL for Hard Decision Decoding using the Welch Berlekamp algorithm is also presented. Without loss of generality, th

A VLSI synthesis of a Reed-Solomon processor for digital communication systems

The Reed-Solomon codes have been widely used in digital communication systems such as computer networks, satellites, VCRs, mobile communications and high- definition television (HDTV), in order to protect digital data against erasures, random and burst errors during transmission. Since the encoding and decoding algorithms for such codes are computationally intensive, special purpose hardware implementations are often required to meet the real time requirements. -- One motivation for this thesis is to investigate and introduce reconfigurable Galois field arithmetic structures which exploit the symmetric properties of available architectures. Another is to design and implement an RS encoder/decoder ASIC which can support a wide family of RS codes. -- An m-programmable Galois field multiplier which uses the standard basis representation of the elements is first introduced. It is then demonstrated that the exponentiator can be used to implement a fast inverter which outperforms the available inverters in GF(2m). Using these basic structures, an ASIC design and synthesis of a reconfigurable Reed-Solomon encoder/decoder processor which implements a large family of RS codes is proposed. The design is parameterized in terms of the block length n, Galois field symbol size m, and error correction capability t for the various RS codes. The design has been captured using the VHDL hardware description language and mapped onto CMOS standard cells available in the 0.8-µm BiCMOS design kits for Cadence and Synopsys tools. The experimental chip contains 218,206 logic gates and supports values of the Galois field symbol size m = 3,4,5,6,7,8 and error correction capability t = 1,2,3, ..., 16. Thus, the block length n is variable from 7 to 255. Error correction t and Galois field symbol size m are pin-selectable. -- Since low design complexity and high throughput are desired in the VLSI chip, the algebraic decoding technique has been investigated instead of the time or transform domain. The encoder uses a self-reciprocal generator polynomial which structures the codewords in a systematic form. At the beginning of the decoding process, received words are initially stored in the first-in-first-out (FIFO) buffer as they enter the syndrome module. The Berlekemp-Massey algorithm is used to determine both the error locator and error evaluator polynomials. The Chien Search and Forney's algorithms operate sequentially to solve for the error locations and error values respectively. The error values are exclusive or-ed with the buffered messages in order to correct the errors, as the processed data leave the chip

Kodierung von Gaußmaßen

Es sei $gamma$ ein Gaußmaß auf der Borelschen $sigma$-Algebra $mathcal B$ des separablen Banachraums $B$. Für $X:Omega o B$ gelte $P_X=gamma$. Wir untersuchen den mittleren Fehler, der bei Kodierung von $gamma$ respektive $X$ mit $Ninmathbb N$ Punkten entsteht, und bestimmen untere und obere Abschätzungen für die Asymptotik ($N oinfty$) dieses Fehlers. Hierbei betrachten wir zu $r>0$ Gütekriterien wie folgt: Deterministische Kodierung $delta_2(N,r) := inf_{y_1,ldots,y_Nin B}Emin_{k=1,ldots,N}X-y_k^r.$ Zufällige Kodierung $delta_3(N,r) := inf_ u Emin_{k=1,ldots,N}X-Y_k^r.$ Die $(Y_k)$ seien hierbei i.i.d., unabhängig von $X$, und nach $u$ verteilt. Das Infimum wird über alle Wahrscheinlichkeitsmaße $u$ gebildet. Für das Gütekriterium $delta_4(cdot,r)$ wird ausgehend von der Definition von $delta_3(cdot,r)$ $u$ nicht optimal, sondern $u=gamma$ gewählt. Das Gütekriterium $delta_1(cdot,r)$ ergibt sich aus der Quellkodierungstheorie nach Shannon. Es gilt $delta_1(cdot,r) le delta_2(cdot,r) le delta_3(cdot,r) le delta_4(cdot,r).$ Wir stellen folgenden Zusammenhang zwischen der Asymptotik von $delta_4(cdot,r)$ und den logarithmischen kleinen Abweichungen von $gamma$ her: Es gebe $kappa,a>0$ und $binR$ mit psi(varepsilon) := -log P{X1.Let $gamma$ be a Gaussian measure on the Borel $sigma$-algebra $mathcal B$ of the separable Banach space $B$. Let $X:Omega o B$ with $P_X=gamma$. We investigate the average error in coding $gamma$ resp. $X$ with $Ninmathbb N$ points and obtain lower and upper bounds for the error asymptotics ($N oinfty$). We consider, given $r>0$, fidelity criterions as follows: Deterministic Coding $delta_2(N,r) := inf_{y_1,ldots,y_Nin B}Emin_{k=1,ldots,N}X-y_k^r.$ Random Coding $delta_3(N,r) := inf_ u Emin_{k=1,ldots,N}X-Y_k^r.$ The $(Y_k)$ above are i.i.d., independent of $X$, and distributed according to $u$. The infimum is taken with respect to all probability measures $u$. For the fidelity criterion $delta_4(cdot,r)$, starting from the definition of $delta_3(cdot,r)$, $u$ is not chosen optimal, but as $u=gamma$. The fidelity criterion $delta_1(cdot,r)$ is given according to the source coding theory of Shannon. The fidelity criterions are connected through $delta_1(cdot,r) le delta_2(cdot,r) le delta_3(cdot,r) le delta_4(cdot,r).$ We obtain the following connection between the asymptotics of $delta_4(cdot,r)$ and the den logarithmic small deviations of $gamma$: Let $kappa,a>0$ and $binR$ with psi(varepsilon) := -log P{X1

Efficient sphere-covering and converse measure concentration via generalized coding theorems

Suppose A is a finite set equipped with a probability measure P and let M be a ``mass'' function on A. We give a probabilistic characterization of the most efficient way in which A^n can be almost-covered using spheres of a fixed radius. An almost-covering is a subset C_n of A^n, such that the union of the spheres centered at the points of C_n has probability close to one with respect to the product measure P^n. An efficient covering is one with small mass M^n(C_n); n is typically large. With different choices for M and the geometry on A our results give various corollaries as special cases, including Shannon's data compression theorem, a version of Stein's lemma (in hypothesis testing), and a new converse to some measure concentration inequalities on discrete spaces. Under mild conditions, we generalize our results to abstract spaces and non-product measures.Comment: 29 pages. See also http://www.stat.purdue.edu/~yiannis

Méthodes de codage et d'estimation adaptative appliquées aux communications sans fil

Les recherches et les contributions présentées portent sur des techniques de traitement du signal appliquées aux communications sans fil. Elles s’articulent autour des points suivants : (1) l’estimation adaptative de canaux de communication dans différents contextes applicatifs, (2) la correction de bruit impulsionnel et la réduction du niveau de PAPR (Peak to Average Power Ratio) dans un système multi-porteuse, (3) l’optimisation de schémas de transmission pour la diffusion sur des canaux gaussiens avec/sans contrainte de sécurité, (4) l’analyse, l’interprétation et l’amélioration des algorithmes de décodage itératif par le biais de l’optimisation, de la théorie des jeux et des outils statistiques. L’accent est plus particulièrement mis sur le dernier thème

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes

In a coded communication system with equiprobable signaling, MLD minimizes the word error probability and delivers the most likely codeword associated with the corresponding received sequence. This decoding has two drawbacks. First, minimization of the word error probability is not equivalent to minimization of the bit error probability. Therefore, MLD becomes suboptimum with respect to the bit error probability. Second, MLD delivers a hard-decision estimate of the received sequence, so that information is lost between the input and output of the ML decoder. This information is important in coded schemes where the decoded sequence is further processed, such as concatenated coding schemes, multi-stage and iterative decoding schemes. In this chapter, we first present a decoding algorithm which both minimizes bit error probability, and provides the corresponding soft information at the output of the decoder. This algorithm is referred to as the MAP (maximum aposteriori probability) decoding algorithm