$1.$ Be a discrete signal transmitted by the source whose values are defined by the vector given below, measured in mV$,$

Y$($n$)=[2\mathrm{.}6,3,4,5\mathrm{.}3,2,6,5\mathrm{.}7,5\mathrm{.}8,6,7].$The instant errors observed at the reception are given by

E$($n$)=[0\mathrm{.}6,0\mathrm{.}3,0\mathrm{.}4,0\mathrm{.}3,0\mathrm{.}2,0\mathrm{.}6,0\mathrm{.}2,0\mathrm{.}1,0\mathrm{.}3,0\mathrm{.}15].$Detemine:

a$.$The value of the average error;

b$.$The value of the square mean error;

c$.$ The signal on the receiver; and

d$.$The signal$-$to$-$noise ratio of error.

$2.$ Be a compression code used by the source encoder that requires it has $1000$ lines of machine instruction. The processor embedded in the transmitter has $16$ MIPS capacity $($millions of instructions per second$)$ when operated at $16$ MHz$.$ What is the delay that the processing of this compression code will cause?

$3.$ Admitting the code of question $2,$ what can be said in relation to its use for applications such as videoconferencing, assuming transmission time of $50$ milliseconds and decoding equal to that of encoding?

$4.$ Assuming $($considering the code of question $2)$ that the clock cycle instruction typically has $16$ bits; and that $60\%$ of the instructions use $16-$bit data; what will be the memory space required by the codec?

$5.$ Be a $3-$bit binary code of a digital communications system. It is known that the probability of having $3$ equal bits is $5\%$; and the probability of each word with $2$ bits equal to $0$ is $3\%$; the other words have the same probability. Determine the entropy of the code.

$6.$ Be a binary code below

$0000-$ s$0$

$0011-$ s$1$

$1100-$ s$2$

$1001-$ s$3$

What can be said about Hammings distance from the code?

$7.$ Considering the code of question $6,$ how can I define the block code, considering that in each block there are two bits of information? How many errors can the code detect on the receiver?How many errors can the code correct in the detector? What is the efficiency of the code?