Empirical Investigation of The Error-Correcting Performance of A Binary Convolutional Code & Coding Theory, LCDP Code - IT Assignment Help

Assignment Task -                 
 

Task 1: Empirical investigation of the error-correcting performance of a binary convolutional code 

In this task, you need to write a script that performs Monte Carlo simulations to obtain BER  curves in noisy channels: AWGN channel, with BPSK modulation.  

For this task, you will use a convolutional code and the probability of error will be estimated empirically i.e. in the form of BER via Monte Carlo simulations.  

The rate ½ code for this task is given in Figure 1. Assume that the input data sequence k=200  bits (adding 3 terminating bits). Therefore, their code-length is 406. As the decoder, you should implement the Viterbi decoder.  

Task 1.1  

The plot in the same figure: the curve for uncoded BPSK transmission, uncoded BPSK  transmission with Eb/N0 adjusted for the code rate, and the BER plot for your code – Figure 2 shows how your results should be represented.

Task 1.2 

Investigate, the impact of “burst noise” and the impact of the random “interleaver” countermeasure. To simulate the “noise burst” assume that 10 consecutive transmitted symbols will see much higher noise (10dB higher noise energy). For example, the transmitted symbols (101-110) will be subject to the higher noise level (it will have 10dB lower SNR) compared to all other transmitted symbols (1-100 and 111 - 406).

Task 2 LDPC codes  

Investigate the performance of the rate 1/2 LDPC code (400,200) on the same channel as in task one. 

Task 2.1 

Construct your own random low-density parity check matrix for the code. Use regular code construction, chose and discuss the node degrees (variable and check node degrees). An example of a parity check code with an H node degree (4,6) is shown in the figure. Design a  systematic generate a matrix for your code. Detail the steps needed to design the generator matrix. 

1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 

1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 

1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 

1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0

Task 2.2 

Investigate the performance of your LCDP code on edited what goes in this channel (the same  channel then in task one). Detail your results (BER curves) as the function of iterations. Investigate the performance on the same “noise burst” channel than in task 1. discuss what countermeasures against noise “bursts” are possible with LDPC code. 

Compare the performance of your two codes: convolutional code and your LDPC. 

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