Suppose a binary data transmission system has sequences of symbols represented as pulses having ±1values (representing ‘1’, ‘0’ digital info., respectively) at particular sampling instants in time when they are decoded. Furthermore, suppose the symbols are corrupted by additive Gaussian distributed noise with a power of .5 watts (into a 1 ohm load). Assume that the threshold for deciding whether a -1 or +1 volt symbol was transmitted is set at zero volts. Assume that the symbols are transmitted with equal probability at the source.

a. What is the probability, P (1|0), the probability of deciding that a '1' is perceived (declared) at a sampling instant given that a '0' was transmitted?

b. What is P(0|1)?

c. What is the total probability of making an error?...sketch the bi-furcated pdf representing this scenario.

d. Recalculate a) through c) for the case where the symbol levels change to +2.3V and the standard deviation of the Gaussian RV becomes 1.1

e. Now suppose , for the conditions applied for items a) through c) that in addition that there is a DC offset of +.125 volts added to the symbols plus noise. What are the results for a), b), c) in this circumstance?

f. Now remove the DC offset from e) and change the threshold comparison voltage to - .125V and rework. What comments can you make to compare the results of e) and f)?