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Telemetry Data Synchronization
Published in Stephen Horan, Introduction to PCM Telemetering Systems, 2018
The Hamming code is easy to compute but its performance is not exceptional. The cyclic codes are a more powerful group of block error correcting codes in which the valid code words are cyclic shifts of other valid code words. The encoding is performed using a generator polynomial, g(D). D is a delay generator and it can be realized in hardware by using a shift register. The code word, c(D), is generated by: () c(D)=u(D)g(D)mod(DN−1)
Basics of Electrical Communication Systems
Published in P. S. Neelakanta, ATM Telecommunications, 2018
Practical implementation of algebraic codes warrants circuits performing matrix multiplication and comparing the results with binary numbers. An alternative strategy is to use a look-up table. Nevertheless, the circuit complexity persists. As a result cyclic codes were developed which are easier to be implemented. A cyclic code has the property that any cyclic shift is a shift (to the right or left) by one position. The end bit cycles around to the starting side. The cyclic codes can be done via using a generating polynomial, g(X) and a polynomial representation of a number. That is, a polynomial is used to represent a binary number by setting the coefficients equal to the bits of the number. For example, a binary number 1011101 corresponds to a polynomial u(x) = 1 + X2 + X3 + X4 + X6. Suppose g(X) = 1 + X + X3 (=>1101); a code word can be generated in terms of a polynomial v(X) = u(x)g(x). This cyclic code generation concept is used in constructing a popular error-control code. It follows the cyclic redundancy check method, which can be described as follows: Given a k-bit block representing a message, the transmitter generates an n-bit sequence, known as the frame check sequence (FCS), so that the resulting frame, consisting of (k + n) bits, is exactly divisible by some predetermined number. The receiver then divides the incoming frame by that number and, if there is no remainder, it confirms that there was no error.
Data Communication
Published in Sunit Kumar Sen, Fieldbus and Networking in Process Automation, 2017
Linear block codes are a form of block codes that are employed for both error detection and correction. For such a linear block code, the XORing of two valid code words would give rise to another valid codeword. Parity check code and Hamming code are some examples of linear block codes. Parity check code is an error-checking code and it has its own drawbacks and is not used in noisy environments. A Hamming code can correct a single error or detect a double error. It can also detect a burst error. A cyclic code is a special type of linear block code in which if a codeword is cyclically shifted, it would result in another codeword. Cyclic redundancy code (CRC) is a type of cyclic code. If automatic repeat request (ARQ) protocol is used in conjunction with CRC code, then it becomes very effective in reducing the BER of a message. A CRC-16 code may attain one undetected error in every 1014 bits.
Fuzzy Linear Codes
Published in Fuzzy Information and Engineering, 2018
S. Atamewoue Tsafack, S. Ndjeya, L. Strüngmann, C. Lele
A fuzzy code A is a fuzzy -cyclic code if it is a fuzzy -linear code and if it is the image under the generalised Gray map of a cyclic code over the ring .