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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.
A convolutional code that is terminated is also a 'block code' in that it encodes a block of input data, but the block size of a convolutional code is generally arbitrary, while block codes have a fixed size dictated by their algebraic characteristics. Types of termination for convolutional codes include "tail-biting" and "bit-flushing".
e. 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.
In information theory, Shannon's source coding theorem (or noiseless coding theorem) establishes the statistical limits to possible data compression for data whose source is an independent identically-distributed random variable, and the operational meaning of the Shannon entropy. Named after Claude Shannon, the source coding theorem shows that ...
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 .
Coding theory is one of the most important and direct applications of information theory. It can be subdivided into source coding theory and channel coding theory. Using a statistical description for data, information theory quantifies the number of bits needed to describe the data, which is the information entropy of the source.
Solution. An error-correcting code is a way of encoding x as a message such that Bob will successfully understand the value x as intended by Alice, even if the message Alice sends and the message Bob receives differ. In an error-correcting code with feedback, the channel is two-way: Bob can send feedback to Alice about the message he received.
Assuming a channel coding setup as follows: the channel can transmit any of = messages, by transmitting the corresponding codeword (which is of length n). Each component in the codebook is drawn i.i.d. according to some probability distribution with probability mass function Q .