Coding Theory Case Study
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 composition of coding theory such as error detecting, error correcting, hamming distance, perfect codes, generator matrices, parity check matrices and hamming codes all of which will be discussed here.
The first two aspects, error detecting and error correcting can be studied together. When a digital message is transmitted, it is done so by a sequence of 0’s and 1’s which encodes a given message. These messages have the potential of being corrupted by noise. Once a message is written an error-detecting code can be written into the message so that any errors can be detected and corrected before the message reaches its final destination. One of the most common types of error- detecting code is called a parity check. A parity check is “the process that ensure accurate data transmission between nodes during communication. A parity bit is appende to the original data bits to create an even or odd bit number; the number of bits with one value. The source then transmits this data via a link, and bits are checked and verified at the destination. Data is considered accurate if the number of bits (even or odd) matches the number transmitted from the source.” (Janseen, 2014) An example could be the message 1101. We add a 0 or 1 to the end of
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 composition of coding theory such as error detecting, error correcting, hamming distance, perfect codes, generator matrices, parity check matrices and hamming codes all of which will be discussed here.
The first two aspects, error detecting and error correcting can be studied together. When a digital message is transmitted, it is done so by a sequence of 0’s and 1’s which encodes a given message. These messages have the potential of being corrupted by noise. Once a message is written an error-detecting code can be written into the message so that any errors can be detected and corrected before the message reaches its final destination. One of the most common types of error- detecting code is called a parity check. A parity check is “the process that ensure accurate data transmission between nodes during communication. A parity bit is appende to the original data bits to create an even or odd bit number; the number of bits with one value. The source then transmits this data via a link, and bits are checked and verified at the destination. Data is considered accurate if the number of bits (even or odd) matches the number transmitted from the source.” (Janseen, 2014) An example could be the message 1101. We add a 0 or 1 to the end of
Cited: Coding Theory. (2010). Retrieved from Wikipedia: http://en.wikipedia.org/wiki/Coding_theory Generator Matrix. (2014, May 21). Retrieved from Wikipedia: http://en.wikipedia.org/wiki/Generator_matrix Janseen, C. (2014). Parity Check. Retrieved from techopedia: http://www.techopedia.com/definition/1803/parity-check Parity-check Matrix. (2014, April 3). Retrieved from Wikipedia: http://en.wikipedia.org/wiki/Parity-check_matrix Weisstein, E. W. (2014). Error-Correcting Code. Retrieved from Wolfram MathWorld: http://mathworld.wolfram.com/Error-CorrectingCode.html