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In coding theory and information theory, a binary erasure channel (BEC) is a communications channel model. A transmitter sends a bit (a zero or a one), and the receiver either receives the bit correctly, or with some probability P e {\displaystyle P_{e}} receives a message that the bit was not received ("erased") .
The feedback capacity is known as a closed-form expression only for several examples such as the trapdoor channel, [14] Ising channel, [15] [16]. For some other channels, it is characterized through constant-size optimization problems such as the binary erasure channel with a no-consecutive-ones input constraint [17], NOST channel [18].
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.
In contrast, belief propagation on the binary erasure channel is particularly simple where it consists of iterative constraint satisfaction. For example, consider that the valid codeword, 101011, from the example above, is transmitted across a binary erasure channel and received with the first and fourth bit erased to yield ?01?11.
the mutual information, and the channel capacity of a noisy channel, including the promise of perfect loss-free communication given by the noisy-channel coding theorem; the practical result of the Shannon–Hartley law for the channel capacity of a Gaussian channel; and of course; the bit - a new way of seeing the most fundamental unit of ...
A deletion channel is a communications channel model used in coding theory and information theory. In this model, a transmitter sends a bit (a zero or a one), and the receiver either receives the bit (with probability p {\displaystyle p} ) or does not receive anything without being notified that the bit was dropped (with probability 1 − p ...
It is the first code with an explicit construction to provably achieve the channel capacity for symmetric binary-input, discrete, memoryless channels (B-DMC) with polynomial dependence on the gap to capacity. [1] Polar codes were developed by Erdal Arikan, a professor of electrical engineering at Bilkent University.
However, the proof is not constructive, and hence gives no insight of how to build a capacity achieving code. After years of research, some advanced FEC systems like polar code [3] come very close to the theoretical maximum given by the Shannon channel capacity under the hypothesis of an infinite length frame.