Table 1 Overview of notation for JNCC for larger networks

m _s

Number of sources

m _r

Number of relays

R _n

Network coding rate, $R_n=\frac{m_s}{m_s+m_r}$

u,u _r ,u _s

user indices to indicate a user in general, a relay, and a source, respectively

$\mathcal{T}\left(u_r\right)$

Transmission set of relay u _r

$n_{u_r}$

$\left|\mathcal{T}\right(u_r\left)\right|$, i.e., the number of sources helped by relay u _r

${\mathbf{s}}_{u_s}$, ${\mathbf{r}}^{u_r}$

Point-to-point codeword transmitted by source u _s and relay u _r , respectively

L

Code length of all point-to-point codewords

H _p

Parity-check matrix of point-to-point codewords, e.g., $H_p{\mathbf{s}}_{u_s}=\mathbf{0}$

R _c,p

Coding rate of point-to-point codewords

c

Overall codeword, that is, the concatenation of all point-to-point codewords

H

Parity-check matrix of overall codeword

R _c

Coding rate of overall codeword, R _c =R_c,pR _n

H _GLNC

The part of H that relates the relay codewords ${\mathbf{r}}_{u_r}$ to the source codewords ${\mathbf{s}}_{u_s}$

$H_{u_s}^{u_r}$

Matrix to transform ${\mathbf{s}}_{u_s}$ in the relation with ${\mathbf{r}}_{u_r}$ in H_GLNC