Suppose a system uses bipolar symbols such that a data 1 is transmitted as a period at 1 V and a data 0 is transmitted as a period at -1 V, and that at the signal detector the data is recovered using threshold detection at 0 V. Suppose, furthermore, that the system is using the (7, 4) Hamming code and that a received code word on one particular occasion is that shown in Fig. 1. a) What binary data would you get after threshold detection at 0 V? b) Without checking if the received code has an error or not, what would this code be decoded to? c) Now check whether there have been any errors in the received code of part (a), and give the decoded output. (Assume that the probability of there being more than one error in a received code word is negligible.)
Quantization and Resolution
Quantization is a methodology of carrying out signal modulation by the process of mapping input values from an infinitely long set of continuous values to a smaller set of finite values. Quantization forms the basic algorithm for lossy compression algorithms and represents a given analog signal into digital signals. In other words, these algorithms form the base of an analog-to-digital converter. Devices that process the algorithm of quantization are known as a quantizer. These devices aid in rounding off (approximation) the errors of an input function called the quantized value.
Probability of Error
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![Suppose a system uses bipolar symbols such that a data 1 is transmitted as a period at 1 V and
a data 0 is transmitted as a period at −1 V, and that at the signal detector the data is recovered
using threshold detection at 0 V.
Suppose, furthermore, that the system is using the (7, 4) Hamming code and that a received
code word on one particular occasion is that shown in Fig. 1.
a) What binary data would you get after threshold detection at 0 V?
b) Without checking if the received code has an error or not, what would this code be
decoded to?
c)
Now check whether there have been any errors in the received code of part (a), and
give the decoded output. (Assume that the probability of there being more than one
error in a received code word is negligible.)
voltage/V
1
decision instants
Figure 1. The received code word
time](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd6cfd83-a1f0-4893-aab5-856ce0c97e61%2F365515c5-39a6-4d29-a748-ff4a7cdfe1c1%2Fbmm7zso_processed.png&w=3840&q=75)
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