In my book it is mentioned that P[Y]= P(X)* P(Y/X) Where P[Y] is the output probability matrix, P(X)=input probability matrix, P(Y/X)= channel matrix. I understand the physical significance of input probabilities and channel matrix probabilities because any input X can be generated which inturn determines the probabilities of generation of Y. But what do we mean by output probabilities? My question: is there any physical significance of output probabilities without defining which input is producing them?
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1What is your book? – Andy aka Dec 14 '20 at 14:28
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1Pretty sure this book is using this quantity somewhere later on for something practical. – Eugene Sh. Dec 14 '20 at 14:45
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1Almost certain that it's P(Y|X); notation *really* quickly makes a difference in stochastics and information theory: don't just replace characters with similar looking ones. – Marcus Müller Dec 14 '20 at 14:48
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If you're receiving a signal from some distant transmitter, the output probabilities are the only thing you can observe. – The Photon Dec 14 '20 at 15:42
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The physical significance of the the output signal is that it's the thing the receiver can actually observe.
The whole point of a communication system is to convey information about something the receiver can't directly observe (the input signal) through some channel to a receiver. If the receiver already knew the input signal they wouldn't need the communication system, they'd simply act on the information they already had.
If we observe the output of a communication system for some time, we can use statistics to estimate (with some uncertainty) the probabilities of receiving different messages. We only know what messages were sent at the transmitter by using our observations of the output signal and the math you're learning now to estimate them.
The Photon
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