Information Theory and Coding > Channel Capacity > Binary Erasure Channel (BEC)

Binary Erasure Channel (BEC)

If effect of noise (or more usually, loss of signal) may have is to prevent the receiver from deciding whether the symbol was a 0 or a 1. In this case the output alphabet includes an additional symbol, ? , called the “erasure” symbol that denotes a bit that was not able to be detected. Thus for binary input {0 , 1} , the output alphabet consists of the three symbols, {0 , ? , 1}. This information channel is called a binary erasure channel or BEC where

P(b = ? /a = 0) = P(b = ? / a= 1) = q

is the probability of error (also called the “erasure” probability). A BEC is becoming an increasingly important model for wireless mobile and satellite communication channels, which suffer mainly from dropouts and loss of signal leading to the receiver failing to detect any signal.

 

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