Coding Theory Paper
Coding Theory
Patrick C Davis
MTH/221
24 Nov 2014
Gerald Weyand
University of Phoenix
Coding Theory Case Study
When representing, manipulating, and transmitting information, it is crucial to use the sequence of zeros and ones. However, it is often impossible and difficult to prevent errors especially in retrieving, operating, transmitting and storing any form of data. Errors occur from different sources, for instance, human beings, equipment, and communication and electrical interference. In most cases, errors occur into data that has been stored for a long period mostly on magnetic tapes when the tape deteriorates. It is significant to make sure that there is reliable transmission especially when large computer files are hastily transmitted (Rosen, 2012). In addition, reliable transmission should be prioritized when sending data over long distances, for instance, from probes billions of millions away. This essay discusses both error correcting and error detecting codes. Further, it will introduce a significant family of codes useful in correcting errors. The essay will also cover the current applications of coding theory as well as the latest technical developments.
It is always important to recover data that has degraded due to long storage in a tape. There are several techniques from the coding theory that guarantees reliable transmission of data and recovery of the degraded data. Messages that occur in the form of bit strings can be encoded through translating them into code word’s or rather bits strings that are a bit longer. A code is a set of code words (Rosen, 2012). It is possible to detect errors using definite codes. Moreover, as long as not too many errors have been made, it is simple to determine whether at least one or many errors have been introduced after transmitting a bit string. Further, it is simple to correct errors that occur due to the use of codes with redundancy.
The study of codes also known as the coding theory involves error
Patrick C Davis
MTH/221
24 Nov 2014
Gerald Weyand
University of Phoenix
Coding Theory Case Study
When representing, manipulating, and transmitting information, it is crucial to use the sequence of zeros and ones. However, it is often impossible and difficult to prevent errors especially in retrieving, operating, transmitting and storing any form of data. Errors occur from different sources, for instance, human beings, equipment, and communication and electrical interference. In most cases, errors occur into data that has been stored for a long period mostly on magnetic tapes when the tape deteriorates. It is significant to make sure that there is reliable transmission especially when large computer files are hastily transmitted (Rosen, 2012). In addition, reliable transmission should be prioritized when sending data over long distances, for instance, from probes billions of millions away. This essay discusses both error correcting and error detecting codes. Further, it will introduce a significant family of codes useful in correcting errors. The essay will also cover the current applications of coding theory as well as the latest technical developments.
It is always important to recover data that has degraded due to long storage in a tape. There are several techniques from the coding theory that guarantees reliable transmission of data and recovery of the degraded data. Messages that occur in the form of bit strings can be encoded through translating them into code word’s or rather bits strings that are a bit longer. A code is a set of code words (Rosen, 2012). It is possible to detect errors using definite codes. Moreover, as long as not too many errors have been made, it is simple to determine whether at least one or many errors have been introduced after transmitting a bit string. Further, it is simple to correct errors that occur due to the use of codes with redundancy.
The study of codes also known as the coding theory involves error
References: Huffman, W. C., & Pless, V. (2003). Fundamentals of error-correcting codes. Cambridge, U.K: Cambridge University Press. MacWilliams, F. J., & Sloane, N. J. A. (1978). The theory of error-correcting codes. Amsterdam: North-Holland Pub. Co. Roman, S. (1996). An introduction to coding and information theory. New York: Springer. Rosen K. (2012). Coding theory. Retrieved from http://www.mhhe.com/math/advmath/rosen/r5/instructor/applications/ch