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Channel capacity is additive over independent channels. [4] It means that using two independent channels in a combined manner provides the same theoretical capacity as using them independently. More formally, let and be two independent channels modelled as above; having an input alphabet and an output alphabet .
In the channel considered by the Shannon–Hartley theorem, noise and signal are combined by addition. That is, the receiver measures a signal that is equal to the sum of the signal encoding the desired information and a continuous random variable that represents the noise. This addition creates uncertainty as to the original signal's value.
Manning formula. The Manning formula or Manning's equation is an empirical formula estimating the average velocity of a liquid in an open channel flow (flowing in a conduit that does not completely enclose the liquid). However, this equation is also used for calculation of flow variables in case of flow in partially full conduits, as they also ...
The BSC has a capacity of 1 − H b (p) bits per channel use, where H b is the binary entropy function to the base-2 logarithm: A binary erasure channel (BEC) with erasure probability p is a binary input, ternary output channel. The possible channel outputs are 0, 1, and a third symbol 'e' called an erasure.
The channel capacity can be calculated from the physical properties of a channel; for a band-limited channel with Gaussian noise, using the Shannon–Hartley theorem. Simple schemes such as "send the message 3 times and use a best 2 out of 3 voting scheme if the copies differ" are inefficient error-correction methods, unable to asymptotically ...
A binary symmetric channel (or BSCp) is a common communications channel model used in coding theory and information theory. In this model, a transmitter wishes to send a bit (a zero or a one), and the receiver will receive a bit. The bit will be "flipped" with a "crossover probability " of p, and otherwise is received correctly.
The minimum channel capacity can be realized in theory by using the typical set or in practice using Huffman, Lempel–Ziv or arithmetic coding. (See also Kolmogorov complexity .) In practice, compression algorithms deliberately include some judicious redundancy in the form of checksums to protect against errors.
In graph theory, the Shannon capacity of a graph is a graph invariant defined from the number of independent sets of strong graph products. It is named after American mathematician Claude Shannon. It measures the Shannon capacity of a communications channel defined from the graph, and is upper bounded by the Lovász number, which can be ...