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A binary erasure channel with erasure probability is a channel with binary input, ternary output, and probability of erasure . That is, let X {\displaystyle X} be the transmitted random variable with alphabet { 0 , 1 } {\displaystyle \{0,1\}} .
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:
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 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.
Low-density parity-check (LDPC) codes are a class of highly efficient linear block codes made from many single parity check (SPC) codes. They can provide performance very close to the channel capacity (the theoretical maximum) using an iterated soft-decision decoding approach, at linear time complexity in terms of their block length.
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.
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 spread throughout all bits of a code.
Erasure Coding; While technically RAID can be seen as a kind of erasure code, [5] "RAID" is generally applied to an array attached to a single host computer (which is a single point of failure), while "erasure coding" generally implies multiple hosts, [3] sometimes called a Redundant Array of Inexpensive Servers (RAIS). The erasure code allows ...