Skip to main content

Table 1 Summary of parameters

From: Probabilistic cooperative coded forwarding for broadcast transmissions in industrial mobile edge communications

Notation Meaning
\(\lambda\) Node density
\(\delta\) One-hop coverage radius
\(\varphi\) Number of one-hop neighbors / Node degree
\(\rho\) Packet erasure probability
\(\omega\) Forwarding probability of SCPs
\(\omega _\rho\) Equivalent forwarding probability of SCPs under packet erasure probability \(\rho\)
\(\xi\) Coded-and-forwarding probability of arbitrary SCP pairs
\(\eta\) Successful delivery probability
\(\eta _\mathrm{{r}}\) Successful delivery probability of a network with volunteer relay nodes only
\(\eta _\mathrm{{s}}\) Coverage probability of silent nodes by relay nodes
\(W_{\mathbf {0}}\) The set of nodes that can connect to the origin \(\mathbf {0}\)
\(\epsilon\) Fraction of nodes that are not covered in a near-broadcast
\({\varphi _\epsilon }\) Minimum value of \(\varphi\) that a near-broadcast could happen
\(a_\mathrm{{c}}\) Critical mean node degree for continuum percolation
\(x_{{i}}\) ith data packet
\(y_{{j}}\) jth source coded packet (SCP)
\(c_{{j,i}}\) the coding coefficient of the ith data packet in the jth SCP
z Relay coded packet (RCP)
\({G_j}\) Connected forwarding graph of \(y_{{j}}\)
\({V_j}\) Nodes that have received the \(y_{{j}}\)
\({E_j}\) Links that have successfully forwarded \(y_{{j}}\)
\({\mathcal{N}}\left( v \right)\) One-hop neighbors of node v
r Number of decoded SCPs
c Number of received RCPs