Teaching Convolutional Coding using MATLAB in Communication Systems Course

Abstract

Convolutional codes are channel codes, which are extensively used in communication systems like GSM (global system for mobile communications) and Interim standard IS-95. We introduce a strategy to present convolutional codes to students learning wireless communication systems, digital communication or similar courses, without using mathematical structures. In this paper, we will discuss our method to implement convolutional encoding and Viterbi decoding to determine the bit error rate. We have compared its performance under different conditions. To exemplify and illuminate our approach, we have selected a communication channel with rate 1/3 convolutional code. Constrain length is three for both Viterbi hard decision decoding method and Viterbi soft decision decoding method. Results suggest that soft decision decoding has at least 3.24 dB improvements in SNR compared to hard decision decoding for same bit error rate. Also by using soft decision Viterbi decoding on AWGN channel, we have examined various convolutional codes for four different constrain lengths and rates. We find that the first code with rate 1/3 code and constrain length 3 has better bit error rate performance with respect to other coding methods. This means, it gives a lower bit error rate for the same value of signal to noise ratio used in other coding schemes. Thus, to achieve the same bit error rate the first code will require a lower SNR. A lower SNR means a lower transmitter power. However, if we use this code the bandwidth requirement is three times larger compared with an un-coded transmission. For the second coding scheme we have an increase in bandwidth by a factor of 2 and for the third and fourth coding scheme the increase factor is 1.5. We believe this approach and its corresponding results will expose students to conceptual and technical aspects of signal encoding and its analysis.