Z-channel (information theory)

In coding theory and information theory, a Z-channel or binary asymmetric channel is a communications channel used to model the behaviour of some data storage systems. ^[1]

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Table of Contents

1. 10 relations: Bernoulli distribution, Binary entropy function, Binary symmetric channel, Channel capacity, Code, Coding theory, Communication channel, Conditional probability, Information theory, Random variable.

Bernoulli distribution

In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which takes the value 1 with probability p and the value 0 with probability q.

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Binary entropy function

In information theory, the binary entropy function, denoted \operatorname H(p) or \operatorname H_\text(p), is defined as the entropy of a Bernoulli process (i.i.d. binary variable) with probability p of one of two values, and is given by the formula: The base of the logarithm corresponds to the choice of units of information; base corresponds to nats and is mathematically convenient, while base 2 (binary logarithm) corresponds to shannons and is conventional (as shown in the graph); explicitly: Note that the values at 0 and 1 are given by the limit \textstyle 0 \log 0.

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Binary symmetric channel

A binary symmetric channel (or BSCp) is a common communications channel model used in coding theory and information theory. Z-channel (information theory) and binary symmetric channel are coding theory.

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Channel capacity

Channel capacity, in electrical engineering, computer science, and information theory, is the theoretical maximum rate at which information can be reliably transmitted over a communication channel. Z-channel (information theory) and channel capacity are information theory.

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Code

In communications and information processing, code is a system of rules to convert information—such as a letter, word, sound, image, or gesture—into another form, sometimes shortened or secret, for communication through a communication channel or storage in a storage medium.

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Coding theory

Coding theory is the study of the properties of codes and their respective fitness for specific applications. Z-channel (information theory) and Coding theory are information theory.

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Communication channel

A communication channel refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel in telecommunications and computer networking. Z-channel (information theory) and communication channel are information theory.

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Conditional probability

In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) is already known to have occurred.

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Information theory

Information theory is the mathematical study of the quantification, storage, and communication of information.

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Random variable

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events.

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References

[1] https://en.wikipedia.org/wiki/Z-channel_(information_theory)

Also known as Binary asymmetric channel, Z Channel (information theory).

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