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##### Oscar uses his high-speed modem to connect to the...

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**Question**

Oscar uses his high-speed modem to connect to the internet. The modem transmits zeros and ones by sending signals ?1 and +1, respectively. We assume that any given bit has probability p of being a zero. The telephone line introduces additive zero-mean Gaussian (normal) noise with variance ?2 (so, the receiver at the other end receives a signal which is the sum of the transmitted signal and the channel noise). The value of the noise is assumed to be independent of the encoded signal value. (a) Let a be a constant between ?1 and 1. The receiver at the other end decides that the signal ?1 (respectively, +1) was transmitted if the value it receives is less (respectively, more) than a. Find a formula for the probability of making an error. (b) Find a numerical answer for the question of part (a) assuming that p = 2/5, a = 1/2 and ?2 = 1/4.

Paper#13112 | Written in 18-Jul-2015

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