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Exact(18)
where ⊥ denotes orthogonality, Γ R = [ γ1,γ2] T, and Γ 0 = [ h 1 D, h 2 D ] T / ∑ m = 1 2 | h mD | 2. Because of the orthogonality feature of the network coding vector, the system sum rate capacity in the network-coded cooperative mode can be obtained directly from [7] C NCCO = log 1 + ρ ∑ m = 1 2 | h mD | 2 1 + ρ | h RD | 2. (15).
In XORs coding, a coded packet carries both the coding vector information and the encoded data.
In the sink, we construct the matrix T after receiving C coding vector.
When given an input that is a coding vector, B 2 outputs an identical copy of its input.
The work in [9] has proved that optimal XORs encoding decision for wireless broadcast, which decides the coding vector of each coded packet, is an NP-hard problem.
An innovative packet refers to a received packet whose coding vector is not in the span of the coding vectors of all previously received packets.
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Further, a new discriminative dictionary learning algorithm is designed for learning a dictionary from training samples to enhance the discriminative capability of its coding vectors.
Therefore, when decoding u, these w overlapping packets provide additional w linearly independent coding vectors beyond T u.
The common assumption in this kind of studies is that the coding vectors of network coding satisfy the restricted isometry property (RIP) of the compressive sensing.
In order to make (P6) work, we will need a suitable n and, for each X i, a set of coding vectors C i ⊆ 2 X i.
We then reduce the research area and the complexity of the optimization problem by considering only 0 1 coding vectors, i.e., θ i =0 in (8).
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