BEC EXIT

**The Binary Erasure Channel (BEC)** is one of the simplest channel models to analyze performance. Many applications can
be modeled as a **Binary Erasure Channel (BEC)** such as packet transmission losses. In **Binary Erasure Channel (BEC)**
a bit is transmitted as a 0 or 1 and the receiver either receives correct bit with probability $1-\epsilon$
or an erausure with probability $\epsilon$ as shown above.

**The EXIT Chart** analysis is divided into two parts as stated previously:

•* Variable nodes decoder EXIT curve is given as an exact expression:* $$I_{E}^{[V]}=1-\epsilon \, \left(1-I_{A}^{[V]} \right)^{v-1} \:(Regular)$$ $$I_{E}^{[V]}=1-\epsilon \,\sum\limits_{i=1}^{v_{max}} \lambda_i \cdot \left(1-I_{A}^{[V]} \right)^{i-1} \:(Irregular)$$ where $v$
in case of regular is the variable nodes degree (number of 1's in each column of

•* Check nodes decoder EXIT curve is given as an exact expression:* $$I_{E}^{[C]}= \left(I_{A}^{[C]} \right)^{c-1} \:(Regular)$$ $$I_{E}^{[C]}=\sum\limits_{j=1}^{c_{max}} \rho_j \cdot \left(I_{A}^{[C]} \right)^{j-1} \:(Irregular)$$ where $c$ in case of regular is the
check nodes degree (number of 1's in each row of

The check nodes