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At present, we are using 10 bits to encode the data bit. Thus, we can think of this as a Repetition(10, 1) scheme.
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We also are using all 16 combinations of the 4 bit input data sequence (40 bit encoded sequence). Thus, the input data has a minimum hamming distance of 1
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If we combine this fact along with our encoding scheme, the effective minimum hamming distance is 10
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Thus, this encoding scheme can correct upto 4 bits.
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Similarly, if we increase the minimum hamming distance of the input data to 2 by considering only 4 out of the 16 4 bit schemes, the minimum effective hamming distance is now 20, and this can correct upto 9 bits.
- The probability of error of transmission is estimated by taking trials against the ground truth blink sequence
10101010101010101010. - Each bit of the ground truth sequence has a corresponding 10 bit of sensor data. So the ground truth blink sequence corresponds to a 100-bit binary sequence
111111111100000000001111111111... - This sequence was chosen as the ground truth because this sequence capture the transition of the bits from
0 to 1and1 to 0. - Multiple trials of sequences are conducted against the ground truth blink sequence.
- The probability of transmission error was calculated as the hamming distance between the recorded sequence and the ground truth sequence.
- It was observed that the probability of transmission error ranged from 0.1 to 0.4 for various trials. The mean probability comes out to be 0.28
- The probability of error for an encoding scheme can be theoretically calculated with the help of the number of bits that can be corrected.
Input vs Output probability of error
Log plot for the same