ENSC428_13Lee - Cyclic code of GF(q): represent as...

Info iconThis preview shows pages 1–24. Sign up to view the full content.

View Full Document Right Arrow Icon
Channel Coding ENSC 428 – Spring 2007
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Digital Communication System
Background image of page 2
Channel Capacity
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
cont …
Background image of page 4
cont …
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
cont …
Background image of page 6
Channel Coding
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Types of Channel Coding
Background image of page 8
Classes of Block Codes
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Block Codes
Background image of page 10
cont …
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example : (7,4) Hamming Code
Background image of page 12
Properties of Block Codes
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
cont …
Background image of page 14
cont …
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Hamming Distance
Background image of page 16
Decoding of Block Codes
Background image of page 17

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Error Correction Capability
Background image of page 18
Probability of Codeword Error
Background image of page 19

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example : (7,4) Hamming Code
Background image of page 20
Per-bit SNR for Coded System
Background image of page 21

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example : BPSK
Background image of page 22
BER for Coded System ?
Background image of page 23

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Cyclic Code
Background image of page 24
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Cyclic code of GF(q): represent as polynomials over GF(q) of degree less than n. c(X) Cyclic shift: Xc(X) mod X n-1 The lowest monic polynomial, g(X) Denote its degree by m. g(X), Xg(X), , X n-m-1 g(X) are all codewords Viewing as a vector space, they are linearly independent Any codeword c(X)=a(X)g(X)+r(X) , r(X)=0. Thus, called generator polynomial. g(X) divides X n-1...
View Full Document

Page1 / 24

ENSC428_13Lee - Cyclic code of GF(q): represent as...

This preview shows document pages 1 - 24. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online