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The key result states that the capacity of the channel, as defined above, is given by the maximum of the mutual information between the input and output of the channel, where the maximization is with respect to the input distribution.
In information theory, the source coding theorem (Shannon 1948) [2] informally states that (MacKay 2003, pg. 81, [3] Cover 2006, Chapter 5 [4]): N i.i.d. random variables each with entropy H(X) can be compressed into more than N H(X) bits with negligible risk of information loss, as N → ∞; but conversely, if they are compressed into fewer than N H(X) bits it is virtually certain that ...
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.
In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is possible (in theory) to communicate discrete data (digital information) nearly error-free up to a computable maximum rate through the channel.
Rate–distortion theory is a major branch of information theory which provides the theoretical foundations for lossy data compression; it addresses the problem of determining the minimal number of bits per symbol, as measured by the rate R, that should be communicated over a channel, so that the source (input signal) can be approximately reconstructed at the receiver (output signal) without ...
A binary symmetric channel (BSC) with crossover probability p is a binary input, binary output channel that flips the input bit with probability p. 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:
The entropy rate of a data source is the average number of bits per symbol needed to encode it. Shannon's experiments with human predictors show an information rate between 0.6 and 1.3 bits per character in English; [21] the PPM compression algorithm can achieve a compression ratio of 1.5 bits per character in English text.
The complete block has m + n bits of data with a code rate of m/(m + n). The permutation of the payload data is carried out by a device called an interleaver . Hardware-wise, this turbo code encoder consists of two identical RSC coders, C 1 and C 2 , as depicted in the figure, which are connected to each other using a concatenation scheme ...