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USING THE MATLAB COMMUNICATIONS TOOLBOX 1 TO LOOK AT CYCLIC CODING

Wm. Hugh Blanton East Tennessee State University

ABSTRACT

In wireless digital communications, the designer is constantly trying to minimize the probability of bit error rates within certain constraints, most notably signal power limits. One method of compensating for bit errors is the use of error control coding that provides sufficient structure to the signal to provide the location of the error. Error control coding requires circuits capable of performing matrix multiplication and comparing the result of various binary numbers. Although the concepts are relatively simple, the implementation becomes rapidly complex as the length of the code word and the uncoded message increase. As a result, most coding theory uses a (7,4) code in which the code word has seven bits of which four bits contain the information.2 The code results in a manageable number of 128 code words of which only 16 form valid codes. The redundancy is used for error correction. Now suppose a (15,7) code is used allowing 32,768 possible code words for which only 128 are valid information codes. This complexity can be reduced by using several functions in the Matlab Communications Toolbox, providing a unique learning opportunity for the engineering technology student.

INTRODUCTION2

Channel coding refers to the class of signal transformations designed to improve communications performance by enabling the transmitted signals to better withstand the effects of various channel impairments, such as noise, interference, and fading. These signal processing techniques can be thought of as vehicles for accomplishing desirable system trade offs (e.g., error performance vs. bandwidth, power vs. bandwidth).

Much of the theory is based upon the Hamming distance which is defined as the number of bit positions in which two binary words differ. For example, consider the following figure.

010 110

011 111 000 100

001 101

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Blanton, W. (2003, June), Using The Matlab Communications Toolbox To Look At Cyclic Coding Paper presented at 2003 Annual Conference, Nashville, Tennessee. 10.18260/1-2--12334