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38 Chapter 4: Unequal Erasure Protection (UEP) in Network Coding
A
b 2
B
C
b 1 ⊕ b 2
b 2
b 2
F
b 1 ⊕ b 2 b 1
b 1 ⊕ b 2
G
b 1 b 1
D
E
Figure 4.3: Another network coding pattern in a butterfly network
problem, so is our problem. Therefore, in the next section, we will formulate it using such
economic terms as utility, marginal value, and anticipation.
4.4 The Utility of Scalable Data
The “utility” is a numerical value representing the amount of satisfaction that a user
receives from an object. In our case, a “user” simply refers to a receiver, whereas the
term “object” deserves a careful consideration. If we define an object by a layer of scalable
data, it might appear at first that we now have several types of objects, since each layer of
data has different properties. However, for the sake of simplicity and orderliness, we will
treat all the layers as the same type of objects which are arranged in order of importance.
Moreover, each layer corresponds to an inseparable object, i.e., half a layer is considered
meaningless. Thus, the word “layer” to be considered here needs not be the same as the
one defined in any particular technical standard. It simply denotes an inseparable unit
of data symbols.
In this way, our formulation will correspond to the following law of
diminishing marginal utility in economics [6].
Law 4.1 : Law of Diminishing Marginal Utility
1. The utility that each receiver gains from receiving scalable data depends on the number