1251185076

# 1251185076 - ECE 635 Error Detecting and Correcting Systems...

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ECE 635 Error Detecting and Correcting Systems Design and Hardware Implementation By Nagi M. El Naga Department of Electrical and Computer Engineering California State University September, 2009 C Nagi El Naga 1

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Course Objectives - To get you familiar with various error detecting and correcting codes. - To teach you how to select a code for a particular application. - To teach you how to design and implement an error detecting and correcting system to meet a particular specifications. 2
Introduction Information theory is usually thought of as sending information from here to there as in Communication Systems or from now to then as in Storage or Memory Systems . Error detecting and correcting subsystems is one of the important subsystems in any of these two systems. 3

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1. Communications System 2. Storage or Memory Device There is a large similarity between the two systems X X O O Here There Now Then You receive You receive information at information at different place. different times. A major concern of the designer of any of these two systems is to control errors so that reliable reproduction of data can be obtained. 4
Assume an information source of symbols: S 1 , S 2 , S 3 ,S n with a probabilities of occurrence: P 1 , P 2 , P 3 ,P n respectively. These symbols can be alphanumeric (A,B,. ....Y,Z,1,2,. ....9). The main two problems of representing the source alphabet symbols S i in terms of another system of symbols (0 & 1) are: 1. How to represent the source symbols so that their representations are far apart in some suitable sense such that when an error occurs the original symbols can be discovered to be wrong and even possibly corrected. Example. If A is represented by 01101 and B is represented by 01100 Then a single change in the first bit will let A be recognized as B or B be recognized as A. 2. How to represent the source symbols in a minimal form for purposes of efficiency. 5

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Figure 1. shows a typical data communication or storage system which is modeled by: 1. An Information Source: Sends information in a form of symbols (Alphanumeric). 2. Source Encoder: transforms the source output symbols into a sequence "m" of binary symbols, which is called the "information sequence." 3. Channel Encoder: According to some rules it transforms the input information sequence "m" into some larger binary sequence "C" which is called the code word of "m". 4. Modulator: Encodes each output digit of the channel encoder into one of two physical wave forms of duration T seconds. e.g. positive and negative pulses. The reason of modulation is to let the signal carry some information about the synchronizing pulses. 5. Demodulator: Makes a decision for each received signal of duration T to determine whether a 1 or a 0 was transmitted. Its output is a sequence "r" of binary digits which is called a received sequence.
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1251185076 - ECE 635 Error Detecting and Correcting Systems...

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