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Coding Theory Case Study Essay

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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 …show more content…

If the original message were 1001, we would encode that as 10010, since the original message already had n even number of 1’s. When someone receives the message 10101, since there are an odd number of 1’s, we know that an error occurred during transmission. We do not know how many there were or which digit(s) were effected and the parity check does locate them for correction.
Once the errors are located an error-correcting code can begin. An ECC “is an algorithm for expressing a sequence of numbers such that any errors which are introduced can be detected and corrected (within certain limitations) based on remaining numbers.” (Weisstein, 2014) The study of error-correcting codes and the associated mathematics is known as coding theory. Detecting the errors within codes is much easier than actually fixing the errors. The major difference between a parity check is that with error-correction, errors are detected and corrected right then, not just detected. Error correction may generally be realized in two different ways: Automatic repeat request (ARQ). This is an error control technique whereby an error detection scheme is combined with requests for retransmission of erroneous data. Every block of data received is checked using the error detection code used, and if the check fails, retransmission of the data is requested – this may be done repeatedly, until the data can be verified. The other is forward error correction (FEC). Here the sender encodes the data using an

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