Channel capacity in the presence of interference.

Channel capacity in the presence of interference.

If the source has entropy H (x), then due to the fact that during the transmission of information over the communication channel, it is interfered with, the uncertainty in relation to the transmitted signal increases at the receiving end. From (*) it follows that the bandwidth without interference is C = (n / t) * H, where H is the source entropy. The effect of interference can be estimated by the entropy H _y (x) - this is the uncertainty of the transmitted message x relative to the received y. Then the formula for the bandwidth of the communication channel is C = n / T * [H (x) - H _y (x)] _max [bit / s] (**). From (**) it follows that when there is interference, the capacity of the communication channel decreases. H _y (x) is called channel unreliability.

Shannon's formula for a communication channel in the presence of interference.

C≤F * log ₂ (1 + P _c / P _w ). F- frequency bandwidth of the communication channel, P _c   - power source signal, P _W - power source of noise or interference. 1) Knowing F, P _c , P _w , it can be argued that the bandwidth of the communication channel cannot be> than calculated by this formula. Increasing the value of F with wired transmission of information leads to a simultaneous increase in interference, which rarely reduces the efficiency of increasing F. 2) If codes are used that correct the errors, then an arbitrarily high probability of correct transmission of the message by reducing the rate of information exchange can be obtained (by introducing redundancy).

When sending a message, the following actions are performed on the information:

1) creation of information by a source, 2) conversion of information into a digital code, 3) introduction of redundancy (error-correcting coding), 4) modulation, 5) passing through a channel, 6) demodulation, 7) decoding (error correction), 8) conversion of corrected code in a form convenient for the consumer.

The subject of study will be noise-resistant coding.