Tables of convolutional codes
Optimal low-rate convolutional codes
The table below lists optimal low-rate convolutional codes, for $n \in \{ 2, 3, 4 \}$, and small values of degree $\sigma$.
Source: LC04, Tables 12.1 (a)–(c), p. 539–540.
| $n$ | $\sigma$ | $g(D) = [g_0(D) ~ \cdots ~ g_{n-1}(D)]$ | $d_\mathrm{free}$ |
|---|---|---|---|
| $2$ | $1$ | [0o3, 0o1] |
$3$ |
| $2$ | $2$ | [0o5, 0o7] |
$5$ |
| $2$ | $3$ | [0o13, 0o17] |
$6$ |
| $2$ | $4$ | [0o27, 0o31] |
$7$ |
| $2$ | $5$ | [0o53, 0o75] |
$8$ |
| $2$ | $6$ | [0o117, 0o155] |
$10$ |
| $2$ | $7$ | [0o247, 0o371] |
$10$ |
| $2$ | $8$ | [0o561, 0o753] |
$12$ |
| $2$ | $9$ | [0o1131, 0o1537] |
$12$ |
| $2$ | $10$ | [0o2473, 0o3217] |
$14$ |
| $2$ | $11$ | [0o4325, 0o6747] |
$15$ |
| $2$ | $12$ | [0o10627, 0o16765] |
$16$ |
| $2$ | $13$ | [0o27251, 0o37363] |
$16$ |
| $3$ | $1$ | [0o1, 0o3, 0o3] |
$5$ |
| $3$ | $2$ | [0o5, 0o7, 0o7] |
$8$ |
| $3$ | $3$ | [0o13, 0o15, 0o17] |
$10$ |
| $3$ | $4$ | [0o25, 0o33, 0o37] |
$12$ |
| $3$ | $5$ | [0o47, 0o53, 0o75] |
$13$ |
| $3$ | $6$ | [0o117, 0o127, 0o155] |
$15$ |
| $3$ | $7$ | [0o225, 0o331, 0o367] |
$16$ |
| $3$ | $8$ | [0o575, 0o623, 0o727] |
$18$ |
| $3$ | $9$ | [0o1167, 0o1375, 0o1545] |
$20$ |
| $3$ | $10$ | [0o2325, 0o2731, 0o3747] |
$22$ |
| $3$ | $11$ | [0o5745, 0o6471, 0o7553] |
$24$ |
| $3$ | $12$ | [0o2371, 0o13725, 0o14733] |
$24$ |
| $4$ | $1$ | [0o1, 0o1, 0o3, 0o3] |
$6$ |
| $4$ | $2$ | [0o5, 0o5, 0o7, 0o7] |
$10$ |
| $4$ | $3$ | [0o13, 0o13, 0o15, 0o17] |
$13$ |
| $4$ | $4$ | [0o25, 0o27, 0o33, 0o37] |
$16$ |
| $4$ | $5$ | [0o45, 0o53, 0o67, 0o77] |
$18$ |
| $4$ | $6$ | [0o117, 0o127, 0o155, 0o171] |
$20$ |
| $4$ | $7$ | [0o257, 0o311, 0o337, 0o355] |
$22$ |
| $4$ | $8$ | [0o533, 0o575, 0o647, 0o711] |
$24$ |
| $4$ | $9$ | [0o1173, 0o1325, 0o1467, 0o1751] |
$27$ |
Optimal high-rate convolutional codes
The table below lists optimal high-rate convolutional codes, for $n \in \{ 3, 4 \}$, and small values of degree $\sigma$.
Source: LC04, Tables 12.1 (d) and (e), p. 540.
| $n$ | $\sigma$ | $h(D) = [h_0(D) ~ \cdots ~ h_{n-1}(D)]$ | $d_\mathrm{free}$ |
|---|---|---|---|
| $3$ | $2$ | [0o7, 0o5, 0o3] |
$3$ |
| $3$ | $3$ | [0o13, 0o15, 0o17] |
$4$ |
| $3$ | $4$ | [0o27, 0o31, 0o23] |
$5$ |
| $3$ | $5$ | [0o73, 0o57, 0o71] |
$6$ |
| $3$ | $6$ | [0o121, 0o147, 0o123] |
$7$ |
| $3$ | $7$ | [0o241, 0o227, 0o313] |
$8$ |
| $3$ | $8$ | [0o477, 0o631, 0o555] |
$8$ |
| $3$ | $9$ | [0o1327, 0o1423, 0o1051] |
$9$ |
| $3$ | $10$ | [0o3013, 0o2137, 0o2621] |
$10$ |
| $4$ | $2$ | [0o6, 0o7, 0o5, 0o1] |
$3$ |
| $4$ | $3$ | [0o12, 0o15, 0o13, 0o11] |
$4$ |
| $4$ | $4$ | [0o31, 0o37, 0o25, 0o33] |
$4$ |
| $4$ | $5$ | [0o75, 0o57, 0o73, 0o47] |
$5$ |
| $4$ | $6$ | [0o141, 0o133, 0o135, 0o107] |
$6$ |
| $4$ | $7$ | [0o267, 0o315, 0o341, 0o211] |
$6$ |
| $4$ | $8$ | [0o661, 0o733, 0o757, 0o535] |
$7$ |
| $4$ | $9$ | [0o1371, 0o1157, 0o1723, 0o1475] |
$8$ |