Network Coding and Wireless Physical-layer ... - Jacobs University

8 Chapter 2: Introduction to Digital Communication Systems and Networks
2.2 Channel Models
Since channel models are mathematical abstractions of physical channels, they can be
divided into several categories based on two factors, which are the nature of physical
channels and the levels of abstraction used. We will discuss four frequently used channel
models which suit the purpose of this thesis.
2.2.1 Binary Erasure Channel (BEC)
Being proposed in 1955 by Elias [52], binary erasure channels become practical for data
networks, especially after the emergence of the Internet. The model offers no possibility
of transmission errors. It assumes that the data is either received correctly or not received
at all. This assumption can only hold on network level of abstraction, where errors are
assumed to be corrected by the data link layer. In reality, erasures may be caused by
buffer overflows at intermediate routers, mismatching of packets’ internal check-sum, or
packets losing their ways [10].
The model can be illustrated by Fig. 2.3, in which X is the transmitted symbol and
Y is the received one. If the erasure probability is p e , the capacity C of the channel is
given by [73]
C = 1 − p e . (2.1)
X
1−p e
Y
0
0
p e
p e
e
1
1−p e
1
Figure 2.3: Binary Erasure Channel