Press "Enter" to skip to content

Richard E. Blahut's Algebraic Codes on Lines, Planes, and Curves: An Engineering PDF

By Richard E. Blahut

Algebraic geometry is usually hired to encode and decode signs transmitted in communique structures. This ebook describes the basic rules of algebraic coding idea from the point of view of an engineer, discussing a couple of functions in communications and sign processing. The relevant inspiration is that of utilizing algebraic curves over finite fields to build error-correcting codes. the latest advancements are provided together with the speculation of codes on curves, with out using designated arithmetic, substituting the serious concept of algebraic geometry with Fourier remodel the place attainable. the writer describes the codes and corresponding deciphering algorithms in a fashion that enables the reader to judge those codes opposed to functional functions, or to aid with the layout of encoders and decoders. This booklet is proper to working towards verbal exchange engineers and people serious about the layout of recent verbal exchange platforms, in addition to graduate scholars and researchers in electric engineering.

Show description

Read or Download Algebraic Codes on Lines, Planes, and Curves: An Engineering Approach PDF

Similar signal processing books

Download e-book for kindle: Time Frequency Analysis: Theory and Applications by Leon Cohen

That includes conventional assurance in addition to new examine effects that, before, were scattered through the expert literature, this publication brings together—in easy language—the simple principles and strategies which were constructed to review common and man-made indications whose frequency content material adjustments with time—e.

Get Shift Register Sequences: Secure and Limited-Access Code PDF

Shift sign in sequences conceal a wide variety of functions, from radar sign layout, pseudo-random quantity iteration, electronic instant telephony, and lots of different parts in coded communications. it's the basic sector for which the writer, Dr Golomb, got the united states nationwide Medal of technological know-how. This ebook is the 3rd, revised version of the unique definitive ebook on shift sign up sequences which used to be released in 1967, which has been broadly dispensed, learn, and brought up.

Download e-book for kindle: Chipless RFID Based on RF Encoding Particle. Realization, by Arnaud Vena, Etienne Perret, Smail Tedjini

Chipless RFID according to RF Encoding Particle: recognition, Coding and interpreting procedure explores the sector of chipless identity in keeping with the RF Encoding Particle (REP). The e-book covers the potential for amassing details remotely with RF waves (RFID) with absolutely passive tags with out twine, batteries, and chips, or even revealed on paper.

Extra info for Algebraic Codes on Lines, Planes, and Curves: An Engineering Approach

Example text

The ring of univariate polynomials modulo xn − 1, denoted F[x]/ xn − 1 or F ◦ [x], is an example of a quotient ring. In the quotient ring F[x]/ p(x) , which consists of the set of polynomials of degree smaller than the degree of p(x), the result of a polynomial product is found by first computing the polynomial product in F[x], then reducing to a polynomial of degree less than the degree of p(x) by taking the remainder modulo p(x). In F[x]/ xn − 1 , this remainder can be computed by repeated applications of xn = 1.

I=0 (9) Cyclic decimation. Write the spectral index j in terms of a vernier index j and a coarse index j : j =j +nj ; j = 0, . . , n − 1; j = 0, . . , n − 1. Then vn i = 1 n 1 = n n −1 n −1 ω−n i ( j +n j ) ω−n ij Vj +n j j =0 j =0 n −1 n −1 ω−n nij Vj +n j . j =0 j =0 Because ωn = 1, the second term in ω equals 1. Then vn i = 1 n n −1 j =0 γ −i j 1 n n −1 Vj +n j j =0 where γ = ωn has order n . , 16 Sequences and the One-Dimensional Fourier Transform (10) Poisson summation. The left side is the direct computation of the zero component of the Fourier transform of the decimated sequence.

The Fourier transform can also be understood as the evaluation of a polynomial. The polynomial representation of the vector v = [vi | i = 0, . . , n − 1] is the polynomial n−1 v (x) = vi xi . i=0 The evaluation of the polynomial v (x) at β is the field element v (β), where n−1 v (β) = vi β i . i=0 The Fourier transform, then, is the evaluation of the polynomial v (x) on the n powers of ω, an element of order n. Thus component Vj equals v (ω j ) for j = 0, . . , n − 1. If F is the finite field GF(q) and ω is a primitive element, then the Fourier transform evaluates v (x) at all q − 1 nonzero elements of the field.

Download PDF sample

Rated 4.96 of 5 – based on 26 votes