I am trying to understand LOCC operations, but there is something i do not know.

My first question is, what is the difference between a LOCC operation and a LOCC protocoll ?

Second, suppose a state $\rho$, if a LOCC operation applied to it you get an ensemble {$p_i$,$\sigma_i$}, $\rho \overset{\text{LOCC}}{\rightarrow} \{p_i,\sigma_i\}$. How can i describe this $\sigma_i$ in a formular? Is this dependent on the LOCC protocoll wich was used? Is it correct when I say that the index $i$ is generally an index family, because it depends on the number of communication rounds?

best regards