Algebraic Number Theory and Code Design for Rayleigh Fading by F. Oggier, E. Viterbo, Frederique Oggier

By F. Oggier, E. Viterbo, Frederique Oggier

Algebraic quantity idea is gaining an expanding effect in code layout for lots of various coding purposes, comparable to unmarried antenna fading channels and extra lately, MIMO platforms. prolonged paintings has been performed on unmarried antenna fading channels, and algebraic lattice codes were confirmed to be a good instrument. the final framework has been constructed within the final ten years and many specific code buildings in line with algebraic quantity idea at the moment are to be had. Algebraic quantity conception and Code layout for Rayleigh Fading Channels presents an outline of algebraic lattice code designs for Rayleigh fading channels, in addition to an educational advent to algebraic quantity thought. the fundamental evidence of this mathematical box are illustrated through many examples and via computing device algebra freeware with a purpose to make it extra available to a wide viewers. This makes the booklet compatible to be used via scholars and researchers in either arithmetic and communications.

Show description

Read or Download Algebraic Number Theory and Code Design for Rayleigh Fading Channels (Foundations and Trends in Communications and Information Theory) PDF

Best radio operation books

Antennas for Information Super Skyways: An Exposition on Outdoor and Indoor Wireless Antennas (Antennas) (Antennas, 12)

The first target of this e-book is to provide the salient facets of antenna rules and expertise and relate those to instant communications purposes. it's written from a special viewpoint, containing a mixture of issues - concept, layout and functions of outside and indoor antennas followed in sleek instant communique structures.

LTE-Advanced Air Interface Technology

Possibilities are handy for pros desirous to study and observe the newest theories and practices in air interface applied sciences. Written by way of skilled researchers and execs, LTE-Advanced Air Interface expertise completely covers the functionality goals and know-how elements studied via 3GPP for LTE-Advanced.

SolderSmoke -- Global Adventures in Wireless Electronics

SolderSmoke is the tale of a mystery, after-hours existence in electronics. invoice Meara began as an ordinary child, from a typical American city. yet round the age of 12 he took an interest in electronics, and he hasn't ever been a similar. To make issues worse, whilst he bought older he turned a diplomat. His paintings has taken him to Panama, Honduras, El Salvador, the Spanish Basque kingdom, the Dominican Republic, the Azores islands of Portugal, London, and, so much lately, Rome.

Extra info for Algebraic Number Theory and Code Design for Rayleigh Fading Channels (Foundations and Trends in Communications and Information Theory)

Sample text

A particular case of finite extension will be of great importance for us. 5. A finite extension of Q is called a number field. √ Going on with our previous example, observe that a way to2 describe 2 is to say √ that this number is the solution of the equation X −2 = 0. of a polynomial equation Building Q( 2), we thus add to Q the solution √ with integers coefficients. The number 2 is said to be algebraic. 6. Let L/K be a field extension, and let α ∈ L. If there exists a non-zero irreducible monic (with highest coefficient 1) polynomial p ∈ K[X] such that p(α) = 0, we say that α is algebraic over K.

6. [45, p. 51] The discriminant dK of a number field belongs to Z. √ Let us compute the discriminant dK of the field Q( 5). Applying √ the two Q-homomorphisms to the integral basis {ω1 , ω2 } = {1, (1+ 5)/2}, we obtain dK = det σ1 (1) σ2 (1) √ √ 1+ 5 σ1 ( 2 ) σ2 ( 1+2 5 ) 2 = det 1√ 1+ 5 2 1√ 1− 5 2 2 =5. We now define a second invariant of a number field. 14. Let {σ1 , σ2 , . . σn } be the n embeddings of K into C. Let r1 be the number of embeddings with image in R, the field of real numbers, and 2r2 the number of embeddings with image in C so that r1 + 2r2 = n .

4, which give the geometric interpretation of the operations involved in the Sphere Decoder. (1) The sphere is centered at the origin and includes the lattice points to be enumerated, Fig. 2. (2) The sphere is transformed into an ellipsoid in the integer lattice domain, Fig. 3. (3) The rotation into the new coordinate system defined by the Ui ’s enables to enumerate the Zn –lattice points. 1. The Sphere Decoder Algorithm 31 inside the ellipse in Fig. 4 are visited from the bottom to the top and from left to right.

Download PDF sample

Rated 4.80 of 5 – based on 43 votes