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By Lupo D., Payne K.R.

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The channel capacity is measured as the limiting value of this maximum rate when the length of the message tends to infinity: 1 log2 M bps T Then, taking into account previous expressions, C = lim (73) T →∞ C = lim T →∞ 1 1 rT log2 M = lim log2 (μr T ) = lim log2 μ = r log2 μ bps T →∞ T T →∞ T T (74) This calculation considers the channel to be noise free. For instance, in the case of the binary alphabet, μ = 2 and C = r. 12: Find the channel capacity of the telephony channel, assuming that the minimum signal-to-noise ratio of this system is P PN dB = 30 dB and the signal and channel transmission bandwidths are both equal to W = 3 kHz.

One important property of a coding table is that it is constructed in such a way that every codeword is uniquely decodable. This means that in the transmission of a sequence composed of these codewords there should be only one possible way of interpreting that sequence. This is necessary when variable-length coding is used. 1 adds redundancy. 75. 24 bits. As seen in this simple example, a level of compression is possible when the information source is not uniform, that is, when a source generates messages that are not equally likely.

As the source generates r symbols per second, the whole emitted sequence takes n/r seconds. Thus, information will be transmitted at a rate of n H (X ) bps (n/r ) (7) R = r H (X ) bps (8) The information rate is then equal to The Shannon theorem states that information provided by a given DMS can be coded using binary digits and transmitted over an equivalent noise-free channel at a rate of rb ≥ R symbols or binary digits per second It is again noted here that the bit is the unit of information, whereas the symbol or binary digit is one of the two possible symbols or signals ‘0’ or ‘1’, usually also called bits.