Table 3 Overview of notation introduced in the diversity analysis

d _max

Maximum diversity order that can be achieved by any code $\mathcal{C}$ for a fixed m _s and m _r

t _min

Minimum number of times that a source is included in the transmission set of any relay

d _R

An upper bound on the diversity order d, d _R = 1 + t_min

n

Is equal to $n_{u_r}$ in the case that $n_{u_r}$ is fixed by the protocol and thus constant

m

Represents m _s and m _r when m _r = m _s

M

Coding header indicating the presence of the source codewords in all transmissions; depends on $\left\{\mathcal{T}\right(u_r\left)\right\}$

$\mathcal{E}$

Set, collecting the indices of the blocks that are erased in the case of the BBEC

$M_{\mathcal{E}}$

Reduced coding header obtained from M where all erased transmissions have been removed

$\mathcal{ℳ}\left(e\right)$

Collection of all possible matrices $M_{\mathcal{E}}$ when $\left|\mathcal{E}\right|=e$

$r_{M_{\mathcal{E}}}$

Rank of $M_{\mathcal{E}}$

d _M

In some cases, d _M , which depends on M, is an upper bound on the diversity order d