Transcription of AN INTRODUCTION TO ERROR CORRECTING CODES Part 1
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AN INTRODUCTION TO ERROR CORRECTING CODES Part 1
AN INTRODUCTION TO ERROR CORRECTING CODESPart 1 Jack Keil WolfECE 154 CSpring 2008 Noisy Communications Noisein a communications channel can cause errors in the transmission of binary digits. Transmit: 1 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 .. Receive: 1 1 0 11 0 1 0 001 0 0 0 0 1 0 .. For some types of information, errors can be detected and corrected but not in :Transmit:Come to my house at 17:25 ..Receive:Come tcmy houzxat 14:25 ..Making Digits Redundant In binary ERROR CORRECTING CODES , only certain binary sequences (called code words) are transmitted. This is similar to having a dictionaryof allowable words. After transmission over a noisy channel, we can check to see if the received binary sequence is in the dictionary of code words and if not, choose the codeword most similar to what was received. NATURE S ERROR CONTROL CODE Nature s code is a mapping of RNA sequences to proteins.
parity check equations can be written as a matrix called the parity check matrix and is denoted H. • The parity check matrix has r rows and n columns. • The i-j thentry (ith row and j column) in this parity check matrix, h i,j, is equal to 1 if and only if the jth component of a code word is contained in the ith parity check equation.
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