Algorithm 3 RSIN Algorithm
1: N	▹ number of retransmission attempts
2:/* Inputs */
3: $N_{max}$	▹ max number of retransmission attempts
4: $R=\{r_1,r_2,...,r_n\}$	▹ set of available rates
5: D	▹ Packet deadline
6: s	▹ SNR value
7:/* Definitions */
8: $t_{trans}$	▹ packet transmission time
9: $P_{r,opt}$	▹ residual error probability for the optimal rate sequence
10:/* Definitions – Vectors of size $N_{max}$ */
11: ${\overline{P}}_r$	▹${\overline{P}}_r\left[i\right]$: residual error probability when $N=i,i=1\cdots N_{max}$
12: ${\overline{t}}_{trans}$	▹${\overline{t}}_{trans}\left[i\right]$: transmission time when $N=i,i=1\cdots N_{max}$
13: ${\overline{RC}}_{low}$	▹ Vector of rate chains.
14:/* The i-th element, ${\overline{RC}}_{low}\left[i\right]$, contains the retransmission chain of length $N=i$ that ensures the lowest transmission error probability*/
15:/* Outputs */
16: $N_{opt}$	▹ optimal number of retransmissions
17: $R{C}_{opt}=\{r_{opt}^{\left(1\right)},r_{opt}^{\left(2\right)},...,r_{opt}^{\left(N_{opt}\right)}\}$	▹ optimal retransmission chain
18:for$i\leftarrow 1$ to $N_{max}$ do
19:    Running Algorithm 4.
20: end for
21:/* Calculation of $N_{opt}$ and $R{C}_{opt}$ */
22: $N_{opt}\leftarrow 1$
23: $R{C}_{opt}\leftarrow {\overline{RC}}_{low}\left[1\right]$
24: $P_{r,opt}\leftarrow {\overline{P}}_r\left[1\right]$
25:for$i\leftarrow 2$ to $N_{max}$ do
26:    if ${\overline{P}}_r\left[i\right]<P_{r,opt}$ then
27:        $N_{opt}\leftarrow i$
28:        $R{C}_{opt}\leftarrow {\overline{RC}}_{low}\left[i\right]$
29:        $P_{r,opt}\leftarrow {\overline{P}}_r\left[i\right]$
30:    else
31:        Do nothing
32:    end if
33: end for