Code Theory

Coding Theory Case Study

Introduction

The twenty-first century is marked as a digital age movement while data is transmitted from location to location. This rapid movement often results in transmission errors, whereas the receiver is not receiving the same informational data originally transmitted. Errors in transmission are due largely as a result of electrical noise disturbances occurring during the transmission process. Occasionally, the electrical noise may alter the logic level of the transmitted signal.

For example, imagine that you are using your laptop to transfer images to your iPad. This transmission uses a string of 1’s and 0’s. When your iPad receives the data, it usually receives a zero versus a one. Any number of disturbances can affect the transfer of data and cause noise on the channel. This noise could prompt the transmission of false data and erroneous transmissions. This phenomenon is what prompted the study of error-correcting codes and the associated mathematics known as the coding theory.

Error Detecting Codes

Error detecting codes are used to detect errors that potentially happen while data is being transmitted. One example of this is a parity check bit that is added to the end of the string of one’s and zero’s. The determination of whether a zero or a one is added at the end of a string is made by whether it is an even or odd numbered string. If a bit string contains an odd number of one’s then a one is put at the end of the string and if the bit string contains an even number of one’s then a zero is put at the end of the string in a parity check.

Adding this type of error detecting code is advantageous in determining errors if only one bit of data is corrupt, however if two bits of data are corrupt then it will give the semblance of an error-free transmission since it brings the string back to an expected even or odd numbered string.

Parity Check Example

The ISBN code is a common tracking system for...