19 Codings, Errors, Data Compression

19 Codings, Errors, Data Compression - ECE 110 M.-C. Brunet...

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ECE 110 M.-C. Brunet Codings, Error Detection, Compression Handout 19
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ECE 110 M.-C. Brunet Codings, Error Detection, Compression Handout 19 Digital Information : Codings Digital codings: Various Issues Reliability :transmission of information. torage compressing of information. Codings, Error Detection/Correction: Storage : compressing of information. Security : confidentiality of information. Codings : ASCII, Parity Bit, Redundancy code, Bar codes (USPS, UPC), … All are fixed length codes: The same number of bits is used for each code word. Redundant bits are added to each word before the entire message is transmitted. Codings for Compression: Codings : Morse, Huffman, Run-length code M.-C. BRUNET ECE 110 UIUC 19.1 (FAX), MPEG2, MP3… All are variable length codes: A different number of bits is used for each code word. Codings & Error Detection arity of a data: count the number of 1s Parity of a data: count the number of 1s The data to send is separated into words . One bit is Ex: The data 00110 is of even parity (contains two 1s) Parity Bit technique: (adds one redundant bit) added to each word so that each set “word+bit” is of a given parity . Example 1 : Use even parity to transmit all 3-bit words of the data (add the parity bit the right f each word): to the right of each word): 0 1 1 1 0 1 1 0 0 0 0 0 The data to be sent is: 0 1 1 . 1 0 1 . 1 0 0 . 0 0 0 . XOR is an Odd function . XOR ( binary sequence ) = 1 when the sequence contains an Odd number of 1s. Automatic Process (by computer): use XOR M.-C. BRUNET ECE 110 UIUC 19.2 Example 2 : XOR (0110) = Xor [Xor(01), Xor(10)] = XOR (011010) = Xor [Xor(0110), Xor(10)] =
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ECE 110 M.-C. Brunet Codings, Error Detection, Compression Handout 19 Transmission of Data using Parity Bit: Assume Even parity is used. Before transmission, an encoder performs for each word (it adds the parity bit for each word): word Æ word + XOR (word) Data: Transmitter: If Odd parity is used instead, then use XNOR . Example 1 (Cont’d) : Using even parity to transmit all 3-bit words of the data (add the parity bit to the right of each word): 0 1 1 1 0 1 1 0 0 0 0 0 XOR: The data to be sent is: M.-C. BRUNET ECE 110 UIUC 19.3 0 1 1 . 1 0 1 . 1 0 0 . 0 0 0 . Assume Even parity is used. After transmission Wb = (word + bit) is received. Error detection? ecoder erforms on each ord the test: A decoder performs on each word the test: Æ if XOR (Wb) = 1 then Error (it’s odd!) else Ok, and Word = W Receiver: W1 W2 W3 W4 Data: W1 W2 W3 W4 (if all ok) Example 1 (Cont’d) : even parity, 3-bit data. The data received is: 0 1 1 0 1 0 1 0 1 1 0 1 0 0 0 0 Is correction possible? One bit error only can be detected. It is not possible to know which bit position it is (so it cannot be corrected). The only solution is to ask for retransmission of the data. Example 3 : Using even parity (at end of word) the words below have been received. What was the original 3-bit data? M.-C. BRUNET ECE 110 UIUC 19.4 (a) 0110 (b) 1101
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ECE 110 M.-C. Brunet Codings, Error Detection, Compression Handout 19 ASCII Code: (1968) ASCII stands for A merican S tandard C ode for I nformation I nterchange. Each symbol is coded on 7 bits (a 6 a 5 a 4 a 3 a 2 a 1 a 0 ). —table below xample 4 000 001 010 011 100 101 110 111 0000 NUL SOH STX ETX EOT ENQ
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This note was uploaded on 09/16/2009 for the course ECE 110 taught by Professor Haken during the Spring '08 term at University of Illinois at Urbana–Champaign.

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19 Codings, Errors, Data Compression - ECE 110 M.-C. Brunet...

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