MIT16_36s09_lec15

# MIT16_36s09_lec15 - MIT OpenCourseWare http/ocw.mit.edu...

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MIT OpenCourseWare http://ocw.mit.edu 16.36 Communication Systems Engineering Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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16.36: Communication Systems Engineering Lecture 15: Cyclic Codes and error detection Eytan Modiano
Cyclic Codes A cyclic code is a linear block code where if c is a codeword, so are all cyclic shifts of c E.g., {000,110,101,011} is a cyclic code Cyclic codes can be dealt with in the very same way as all other LBC s Generator and parity check matrix can be found A cyclic code can be completely described by a generator string G All codewords are multiples of the generator string In practice, cyclic codes are often used for error detection (CRC) Used for packet networks When an error is detected by the received, it requests retransmission

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Error detection techniques Used by the receiver to determine if a packet contains errors If a packet is found to contain errors the receiver requests the transmitter to re-send the packet Error detection techniques Parity check E.g., single bit Cyclic redundancy check (CRC)
Parity check codes k Data bits r Check bits Each parity check is a modulo 2 sum of some of the data bits Example: c 1 = x 1 + x 2 + x 3 c 2 = x 2 + x 3 + x 4 c 3 = x 1 + x 2 + x 4

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MIT16_36s09_lec15 - MIT OpenCourseWare http/ocw.mit.edu...

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