Keywords

Error Correction, Bit Error Rate, 3g Network, Convolution Code, Transmission Over.

Introduction

The last thirty five years have seen a dramatic change in the way communication is achieved around the world. Wireless communication has evolved from being an expensive and rare technology for the few in the 70’s to becoming a wide spread and economical means of facilitating commercial as well as public service communications. One of the majors reasons for the continuous growth in the use of wireless communication is its increasing ability to provide efficient communication links to almost any location, at constantly reducing costs with increasing power efficiency (Jemibewon, 2000). Wireless communication is one of the most active areas of technological development. This development is being driven primarily by the transformation of what has been a medium for supporting voice telephone into a medium for supporting other services such as transmission of video, images, text and data etc (Wang, 2003). Basically, a communication system deals with information or data transmission from one point to another (Du, 2009). Over the years, there has been a tremendous growth in digital communications especially in the fields of cellular, satellite and computer communications. In these communication systems, the information is represented as a sequence of binary bits. The binary bits are then mapped (modulated) to analog signal wareforms and transmitted over a communication channel. The communication channel introduces noise and interference to corrupt the transmitted signal. At the receiver end, the channel corruptedtransmitted signal is mapped back to binary bits. The received binary information is an estimate of the transmitted binary information (Huang, 1997). Normally, during signal transmission through noisy channels errors can be detected and corrected using coding techniquesHuang, 1997). Noise is any undesired signal in a communication circuit. Noise can also be unwanted disturbances supper imposed on a useful signal, which tends to obscure its information content.

Formulation of an experimental simulation mode

Structure of model formed to simulate the convolution encoder is shown below

Figure 1: Structure of the Model Used to Simulate he Convolution encoder

Firstly, the Bernoulli Binary Generator generates bits or symbols to be compared and the convolution encoder codes the generated bits and detect the error involved in accordance with the convolution encoder characteristics. These values are recorded and tabulated as shown in table 2.1, 2.2, and 2.3 below. These are for code rate ½ 1/3 and uncoded system. these values were obtained with the assistance of Globacom Technical Workers in their office in Umuahia. The equipment used is known as the Transmission Test Set (TTS).3

Table 1

Measured Data in Coded System for Code Rate ½

S/N No of symbols compared No of errors detected
1 50 2
2 51 2
3 52 2
4 53 2
5 54 2
6 55 2
7 56 2
8 57 2
9 58 2
10 59 2

Table 2

Measured Data in Coded System for code rate 1/3

S/N No of symbols compared No of errors detected
1 50 3
2 51 3
3 52 3
4 53 3
5 54 3
6 55 3
7 56 3
8 57 3
9 58 3
10 59 3

Table 3

Measure data for Uncoded System

S/N No of symbols compared No of errors detected
1 50 23
2 51 24
3 52 24
4 53 25
5 54 25
6 55 26
7 56 26
8 57 27
9 58 28
10 59 28

Table 4

Simulated data in coded system for code rate ½ with Ber

S/N No of Symbols Compared No Of Errors Detected Bit Error Rate (BER)
1 50 2 0.04
2 51 2 0.03922
3 52 2 0.03846
4 53 2 0.03774
5 54 2 0.03704
6 55 2 0.03636
7 56 2 0.03571
8 57 2 0.03509
9 58 2 0.03448
10 59 2 0.0339

Figure 2: Graph of the Simulation Data in Coded System for Code Rate ½

Table 5

Simulated data in coded system for code rate ½ with BER

S/N No of Symbols Compared No Of Errors Detected Bit Error Rate
1 50 3 0.06
2 51 3 0.05882
3 52 3 0.05769
4 53 3 0.0566
5 54 3 0.05566
6 55 3 0.05455
7 56 3 0.05357
8 57 3 0.05263
9 58 3 0.05172
10 59 3 0.05085

Figure 3: Graph of the Simulation Data in Coded system for code Rate ½

Table 6

Comparison of simulated coded data (½, 1/3) with Bit Error Rate

S/N ½ coded BER 1/3 Coded BER
1 0.04 0.06
2 0.0392 0.0588
3 0.0385 0.0577
4 0.0377 0.0566
5 0.037 0.0556
6 0.0364 0.0545
7 0.0357 0.0536
8 0.0351 0.0526
9 0.0345 0.0517
10 0.0339 0.0508

Figure 4:Graph of Simulated Data in coded system for code rate 1/3

Data analysis

From the simulation results in table 4.1, 4.2, 4.3, it can be seen that with an increase in number of symbols compared, there is a decrease in bit error rate. The starting points of the bit error rate (BER) for ½ and 1 /3 codes are 0.040 and 0.060 respectively. These decease linearly to the end point of 0.0339 and 0.05085. When ½ , 1 /3 codes are compared with uncoded system which has a bit error rate (BER) start from 0.0460 and ended at 0.4746, it is seen to be about 60% more than the coded system.

Conclusion

With the detailed description of the convolution code coder and decoder presented in chapter three, the performance of convolution codes was investigated through extensive computer simulation. The validate the convolution codes simulation, comparisons were made between the coded graphs, it is evident that there was a 60% and 65% improvement on coding gains for the two code rates used. This improvement can be attributed to the introduction of the convolution codes. In general, it is observed that the introduction of the convolution coding scheme has helped to decrease the Bit Error Rate significantly which in turn will result in the transmission of signals of specified quality with a smaller transmit power. In other words, it leads to higher power efficiency, but on the other hand, the bit error rate is half or one third of the uncoded scheme thus lowering bandwidth efficiency. It can then be concluded that a coded system offers better channel efficiency uncoded system.