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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") .
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 basic mathematical model for a communication system is the following:
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. The erasure represents complete loss of information about an input bit. The capacity of the BEC is 1 − p bits per channel use.
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 ...
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.
Just as the shannon describes the maximum possible information capacity of a binary symbol, the hartley describes the information that can be contained in a 10-ary symbol, that is, a digit value in the range 0 to 9 when the a priori probability of each value is 1 / 10 . The conversion factor quoted above is given by log 10 (2).
Shannon's definition of entropy, when applied to an information source, can determine the minimum channel capacity required to reliably transmit the source as encoded binary digits. Shannon's entropy measures the information contained in a message as opposed to the portion of the message that is determined (or predictable).
In telecommunications, the channel capacity is equal to the mutual information, maximized over all input distributions. Discriminative training procedures for hidden Markov models have been proposed based on the maximum mutual information (MMI) criterion. RNA secondary structure prediction from a multiple sequence alignment.