# Dr Jerzy Rutkowski

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## Kody blokowe - podstawowe pojęcia i definicje

• Politechnika Śląska
• Teoria informacji i kodowania
Pobrań: 21
Wyświetleń: 1218

Block codes Basic concepts and definitions A source information is processed, first, in a channel encoder, next, in a discrete memoryless channel and finally, in a channel decoder, as presented in Fig.5.1.1. The output sequence ; , is the result of mod-2 addition of a codeword ; , and error patter...

## Pojemność kanału

• Politechnika Śląska
• Teoria informacji i kodowania
Pobrań: 0
Wyświetleń: 1288

Channel capacity Channel capacity of DMC is defined as the largest mutual information that can be transmitted over the channel in one use, maximized over all input probability assignments . It is worth to observe that, whereas is a function of both the channel and the input probability assignment,...

## Budowa matrycy generatora RM

• Politechnika Śląska
• Teoria informacji i kodowania
Pobrań: 0
Wyświetleń: 6895

Construction of the generator matrix of a RM( r , p ) code Step 0. The first row of G is the all-1 codeword: . Step 1. The next rows, the 1 st order codewords, form submatrix 0 1 n 1 The l -th column is the integer l in the binary code: . Step 2. The next rows, the 2 nd order codewords, fo...

## Dekodowanie kodów cyklicznych

• Politechnika Śląska
• Teoria informacji i kodowania
Pobrań: 0
Wyświetleń: 896

Decoding cyclic codes Following the Conclusion to check whether the received sequence is a code word of an cyclic code, is divided by , a reminder is designated. This reminder can be considered as syndrome polynomial of , and it determines a decoder decision, following the strategy of (5.2.25) for...

## Extended linear code

• Politechnika Śląska
• Teoria informacji i kodowania
Pobrań: 0
Wyświetleń: 917

Extended linear code Error control capability of an linear code can be improved by adding an overall parity-check bit. An extended code is obtained. The addition of such bit increases a code minimum distance by one. For the Hamming extended code: , what enables single-error correction and also doub...

## Opis kodowania i dekodowania

• Politechnika Śląska
• Teoria informacji i kodowania
Pobrań: 7
Wyświetleń: 910

General description Encoding and decoding An linear code is called a cyclic code if a cyclic shift of any codeword is also a codeword. The shift may be leftwards or rightwards, by any number of bits. The cyclic code nature can be utilized when encoding and decoding, using linear-feedback shift reg...

## Generator i kontrola parzystości kodów cyklicznych

• Politechnika Śląska
• Teoria informacji i kodowania
Pobrań: 7
Wyświetleń: 1771

Generator matrix and parity check matrix of cyclic codes Generator matrix consists of algebraically independent subset of k codewords. These words can be words with weight of information part equal 1, i.e. words with information bits encoding integers: , in polynomial notation: . Then, following st...

## Generator matrix

• Politechnika Śląska
• Teoria informacji i kodowania
Pobrań: 0
Wyświetleń: 1239

Generator matrix Any algebraically independent subset of k nonzero codewords uniquely defines an ( n , k ) linear code. Such subset consists a code-base, that can be considered as rows of the so called generator matrix: To obtain all possible combinations of generator matrix rows, matrix G has to ...

## Generator wielomianu

• Politechnika Śląska
• Teoria informacji i kodowania
Pobrań: 7
Wyświetleń: 1442

Generator polynomial Consider nonzero codeword of a cyclic code having the smallest degree of its polynomial, i.e. having the longest all-zero sequence at first (leftmost) bits: . For the considered cyclic code (7,4), defined by parity-check matrix (7.1.1), : . Each cyclic shift of this word is als...

## Hamming code 7 4

• Politechnika Śląska
• Teoria informacji i kodowania
Pobrań: 7
Wyświetleń: 1169

Hamming code 7 4 is the first code in the class of Hamming codes. Error syndromes, corresponding to single-error patterns, are written as binary words: that encode a position of nonzero bit in z , as presented in Table i 1 1 001 2 01 010 3 001 011 4 0001000 100 5 100 101 6 10 110...