early stopping method

8/6/2019 Early Stopping Method

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Early Stopping Method


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In the next figures, the Bit Error Rate (BER) is plotted as a function ofSignal-to-Noise Ratio (SNR) and Number of Iterations (ITER). From thesedata is possible to get 3-dimensional graphs for different sizes of Z andfor both quantized and un-quantized cases.


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A better way to represent the data is plotting BER as a function of SNR,parameterized with different values of Iterations. In particular a log10scale has been used for the BER.


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Z = 48QUANTIZED


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Z = 48UN-QUANTIZED


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Z = 24UN-QUANTIZED


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Z = 24QUANTIZED


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As shown in the previous figures, increasing the

number of iterations (ITER), the curves tend tobe more and more close, i.e. the gain of SNR indB decrease increasing ITER. So it is possibleplotting distances between these curves (for a

fixed value of BER = 1e-5) as a function ofITER. An estimation of the trend of the curveshas been done in order to get the SNR valuescorresponding to the BER = 1e-5. In particular

the matlab function polyfit and polyvalhave been used to achieve this aim. Thepolynomial degree used to fit these curves isN=3.


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In the next figures, the Parity Check Errors (PCE) is plotted as a functionof Signal-to-Noise Ratio (SNR) and Number of Iterations (ITER). Fromthese data is possible to get 3-dimensional graphs for different sizes of Zand for both quantized and un-quantized cases.


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As before, a better way to represent the data is plotting Parity CheckErrors as a function of SNR, parameterized with different values ofIterations. In particular a linear scale has been used for the Parity CheckErrors .


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As before, using the matlab functions polyfitand polyval fitting has been done and Gainas function of ITER has been plotted. Now, thedifference is that Gain-vs-ITER can be plottedafter that a fixed value for Parity Check Errors

has been choosen.

So I thought to figure out a correspondencebetween BER=1e-5 and Parity Check Errors.

The idea is plotting BER and Parity Check Errorsin the same firgure, both as a function of ITER.


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When ITER is 18, the correspondent BER value is about 1e-5. In the sametime, for ITER=18 the number ofParity Check Errors is about 0,005.As usual, the Parity Check Error values are normalized with the numberof codeword (blocks) analyzed.


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Conclusions

If you have a look at the graphs reporting Gain [dB]

vs Number of Iteration, in both cases (Bit Error Rate

and Parity Check Errors evaluation) the Gaindecreases increasing the Number of Iterations. In

particular after 10 iterations, the Gain is always

smaller then 0,01 dB. So the idea would be to halve

the number of Iterations, granting a Bit Error Rate of

1e-5.

early stopping method

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