Richard E. Blahut's Algebraic codes for data transmission PDF

Posted by

By Richard E. Blahut

ISBN-10: 0511077408

ISBN-13: 9780511077401

ISBN-10: 0521553741

ISBN-13: 9780521553742

Error-correcting codes play a primary position in sleek communications and data-storage structures. This quantity offers an available creation to the fundamental components of algebraic codes and discusses their use in quite a few purposes. the writer describes a variety of very important coding concepts, together with Reed-Solomon codes, BCH codes, trellis codes, and turbocodes. through the publication, mathematical conception is illustrated by means of connection with many sensible examples. The booklet is written for graduate scholars of electric and laptop engineering and practising engineers whose paintings consists of communications or sign processing.

Show description

Read or Download Algebraic codes for data transmission PDF

Similar signal processing books

Download PDF by Lemuel Ibbotson: The Fundamentals of Signal Transmission: Optical Fibre,

'The basics of sign Transmission' offers a dialogue of the most kinds of sign transmission media. Twisted pair, coaxial line, optical fibre, waveguides and freespace propagation and antennas are lined utilizing a typical layout. After a dialogue of indications quite often, the character of wave propagation is tested.

Download e-book for iPad: Introduction to Digital Communications by Ali Grami Ph.D.

Creation to electronic Communications explores the elemental rules within the research and layout of electronic communique structures, together with layout targets, constraints and trade-offs. After portraying the massive photograph and laying the history fabric, this booklet lucidly progresses to a finished and distinctive dialogue of all severe parts and key features in electronic communications.

Additional info for Algebraic codes for data transmission

Example text

The polynomial D(x) has at most µ − 1 zeros. The coefficient dµ−1 is itself the determinant of a Vandermonde matrix, and by the induction hypothesis, is nonzero. If for any i, 2 ≤ i ≤ µ, we set x = X i , then two rows of the matrix are equal, and D(X i ) = 0. Thus for each i = 1, X i is a zero of D(x), and because they are all distinct and there are µ − 1 of them, the polynomial can be easily factored: µ D(x) = dµ−1 (x − X i ) . i=2 Therefore the determinant of the original Vandermonde matrix is µ D(X 1 ) = dµ−1 (X 1 − X i ) .

Find a set of sixteen binary words of length 7 such that each word is at least a distance of 3 from every other word. 2 a. 5 inches and length 11 inches. Prove that it is not possible to cut out more than 119 circles of 1-inch diameter. b. Prove that it is not possible to find 32 binary words, each of length 8 bits, such that every word differs from every other word in at least three places. 3 A single-error-correcting Hamming code has 2m − 1 bits of which m bits are check bits. a. Write (n, k) for the first five nontrivial Hamming codes (starting at m = 3).

J = 1, . . , m. This matrix product is denoted as C = AB. With this definition of matrix multiplication, and the earlier definition of matrix addition, the set of n by n square matrices over any field F forms a ring, as can be easily verified. It is a noncommutative ring, but it does have an identity, namely the n by n identity matrix. A matrix can be partitioned as follows: A= A11 A21 A12 A22 where A11 , A12 , A21 , and A22 are smaller matrices whose dimensions add up to the dimensions of A in the obvious way.

Download PDF sample

Algebraic codes for data transmission by Richard E. Blahut


by William
4.1

Rated 4.59 of 5 – based on 20 votes