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Table 1 Main notations and their descriptions

From: Instantly decodable network coding for real-time scalable video broadcast over wireless networks

  Description   Description
Q Number of remaining transmissions L Number of video layers
\(\mathcal {M}\) Set of M receivers \(\mathcal {N}^{1:\ell }\) Set of N 1: packets
R i The ith receiver in \(\mathcal {M}\) P j The jth packet in \(\mathcal {N}\)
F 1: M×N 1: state feedback matrix ω th window among L windows
\(\mathcal {H}_{i}^{1:\ell }\) Has set of receiver R i in the first layers \(\mathcal {W}_{i}^{1:\ell }\) Wants set of receiver R i in the first layers
\(T_{W_{i}^{1:\ell }}\) Individual completion time of receiver R i for layers T 1: Individual completion times of all receivers for layers
\(\mathcal { G}^{1:\ell } \) IDNC graph constructed from F 1: \(T_{B}^{1:\ell }\) Individual completion times of all non-critical receivers for layers
\(\mathcal {C}^{1:\ell }\) Critical set of receivers for the first layers \(\mathcal {A}^{1:\ell }\) Affected set of receivers for the first layers
\(\mathcal {B}^{1:\ell }\) Non-critical set of receivers for the first layers \(\mathcal {M}_{w}^{1:\ell }\) Set of receivers having non-empty Wants sets in the first layers
v ij A vertex in an IDNC graph induced by missing packet P j at receiver R i \(\mathcal {X}(\kappa)\) Set of targeted receivers in maximal clique κ