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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.
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. Since the transmitted message must have satisfied the code constraints, the message can be represented by writing the received message on the top of the ...
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.
For example, a 1,000,000-digit binary one-time pad using exclusive or. If the pad has 1,000,000 bits of entropy, it is perfect. If the pad has 1,000,000 bits of entropy, it is perfect. If the pad has 999,999 bits of entropy, evenly distributed (each individual bit of the pad having 0.999999 bits of entropy) it may provide good security.
Graph showing the proportion of a channel’s capacity (y-axis) that can be used for payload based on how noisy the channel is (probability of bit flips; x-axis). The channel capacity of the binary symmetric channel, in bits, is: [2] = (),
For the case of channel capacity, the algorithm was independently invented by Suguru Arimoto [1] and Richard Blahut. [2] In addition, Blahut's treatment gives algorithms for computing rate distortion and generalized capacity with input contraints (i.e. the capacity-cost function, analogous to rate-distortion). These algorithms are most ...