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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.
To make an optimal code, the two transfer curves need to lie close to each other. This observation is supported by the theoretical result that for capacity to be reached for a code over a binary-erasure channel there must be no area between the curves and also by the insight that a large number of iterations are required for information to be ...
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.
These are examples of commonly used channel capacity and performance measures: Spectral bandwidth in Hertz; Symbol rate in baud, symbols/s; Digital bandwidth in bit/s measures: gross bit rate (signalling rate), net bit rate (information rate), channel capacity, and maximum throughput; Channel utilization; Spectral efficiency
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.
The parity bit may be used within another constituent code. In an example using the DVB-S2 rate 2/3 code the encoded block size is 64800 symbols (N=64800) with 43200 data bits (K=43200) and 21600 parity bits (M=21600). Each constituent code (check node) encodes 16 data bits except for the first parity bit which encodes 8 data bits.