Essay on Coding Theory

Coding theory is the study of the properties of codes and their corresponding fitness for the specific application. The theory which has its inception in the late 1940s is currently identified as a mature science. Coding theory has been applied in various disciplines ranging from technology, mathematics, applied sciences among others.

First, coding theory is used inline code which is utilized in the transmission of the digital signal over a transmission line. Error coding has been used intensively in digital communication since it is cost-effective in achieving effectiveness and reliability in digital transmission. At the moment, coding plays an essential role in designing the current communication system. Transmitted messages such as data from a satellite are frequently subjected to noise hence causing the error to take place at the decoder input. This done mostly through repeating messages more than one times which is common in human speech. It is therefore essential to be capable of encoding the message in a manner that after noise scrambles on the way, it can be decoded to its original form (Grossman,2008). A natural design aim is to choose the code in such a way that various errors were occurring at the decoder input can be corrected by the decoder, thereby providing a suitable level of dependability. There are fundamental coding techniques that are used in the communication system. Various messages are sent as digital-sequence of 0s and 1s, for instance, 10101. Assuming that a message sent is 1011; such binary word might stand for an actual word such as go. To encode 1011, a binary tail tail can be attached to it so that in the vent that the message gets distorted too, say, 0111, an error can be detected easily. One such tail can be 1 or 0 depending on whether an even number of 1s in the word. As such, all encoded words will have the even number of 1's. Therefore, 1001 will be encoded as 10111 and in the event of a distortion, an error can easily be detected(Grossman,2008).

Second, coding theory is applied in computational complexity. The interplay coding theory and computation complexity theory is a rich source of results and problems. Complexity theory focuses on efficient computation. However, the theory is faced with a lot of computational problems which can be modeled formally, and a complication theorist tries to first to the solution which is probably useful and, if not a solution is not identified, to prove that none exists. In such a scenario, coding theory has been used in designing efficient solutions and providing that practical solution that does not exist through the provision of techniques for robust representation of information (Grossman,2008).

Third ,coding theory is used in cryptographical coding which is a practice and study of techniques for securing information. There are many problems in cryptography to which well-developed techniques and general results of coding theory can be applied abundantly. Application of coding theory to cryptography entails the introduction of the new coding concept that might well be essential to its right. For instance, the use of minimal codewords in linear codes that are significant in treating secret-sharing schemes with tailored access privileges. Cryptographical coding entails construction and evaluation of protocols which block different aspects of information security such as data integrity and confidentiality (Adamek,2011). In this information age, the requirement to protect data is more pronounced than ever. As the world continues to be more connected, there is an increased demand for information and electronic devices and this increased demand is accompanied with increased dependency on an electronic system. Currently, the exchange of sensitive information such as credit card number over the internet is widespread. Current cryptography exists at the connection of disciplines of computer science, mathematics among others. The modern cryptography deeply based on mathematical theory and computer science practice. Cryptography is designed around computational hardness assumption an this make it hard for unauthorized individuals from breaking such algorithm. It is evident that breaking such system is theoretically possible; however, it is not feasible to carry it out by practices that are recognized (Joyner,2012).

Lastly, a coding theory has also been applied in group testing. Group testing is a set of problems with the aim of reducing the cost of identifying particular elements. The origin of group testing has its roots in the WWW11 when united states public health service required to test soldiers for syphilis. However, testing syphilis during that particular period was expensive and testing every individual was wasteful. Group testing aimed to find individuals suffering from syphilis with the smallest number of testing and this attracted coding whereby a certain number of soldiers were grouped and given a particular code. In this case, the total number of a soldier is n while an upper bound on the number of infected soldiers is d. The unidentified information regarding which soldiers are infected can be described as a vector where if the item is infected else (Grossman,2008).

References

Adamek, J. (2011). Foundations of coding: Theory and applications of error-correcting codes with an introduction to cryptography and information theory. John Wiley & Sons.

Grossman, J. (2008). Coding theory: introduction to linear codes and applications. Insight: River Academic Journal, 4(2), 1-17.

Grossman, J. (2008). Coding theory: introduction to linear codes and applications. Insight: River Academic Journal, 4(2), 1-17.

Joyner, D. (Ed.). (2012). Coding theory and cryptography: from Enigma and Geheimschreiber to quantum theory. Springer Science & Business Media.