Coding Theory Case Study

1085 words 5 pages
Coding Theory Case Study
Alicia Griffin
MTH 221
June 9, 2014
Howard Thomas
Coding Theory Case Study
What is Coding Theory? “Coding theory is the study of the properties of codes and their fitness for a specific application. Codes are used for data compression, cryptography, error-correction and more recently also for network coding. Codes are studied by various scientific disciplines – such as information theory, electrical engineering, mathematics, and computer science – for the purpose of designing efficient and reliable data transmission methods. This typically involves the removal of redundancy and the correction (or detection) of errors in the transmitted data.” (Coding Theory, 2010) There are many aspects that go into the
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In general, the reconstructed data is what is deemed the “most likely” original data. By combining both of these concepts, minor errors are corrected without retransmission and major errors are corrected via a request for retransmission.
In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different. In another way, it measures the minimum number of substitutions required to change one string into the other, or the minimum number of errors that could have transformed one string into the other. Some examples of the Hamming distance are: “karolin” and “kathrin” is 3, “karolin” and “kerstin” is 3, 1011101 and 1001001 is 2 and 2173896 and 2233796 is 3. The Hamming distance is named after Richard Hamming, who introduced it in his fundemental paper on Hamming codes in 1950. Hamming weight analysis of bits is used in several disciplines including information theory, coding theory, and cryptography. Codes that attain the Hamming bound are called perfect codes. An example is given by the repeat codes, where each symbol of the message is repeated an odd fixed number of times to obtain a codeword where q=2. Hamming (7,4) is a linear error-correcting code that encodes 4 bits of data into 7 bits by adding 3 parity bits. It is a member of a larger family of Hamming codes, but the term Hamming code often refers to the code that he invented in 1950. The


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