Joint coding and modulation achieving coding gain without bandwidth expansion. Combines convolutional encoding with signal constellation mapping using set partitioning. Invented by Gottfried Ungerboeck at IBM Zurich. Used in V.32/V.34 modems, digital satellite communications, and wireless systems. Viterbi decoding on trellis maximizes Euclidean distance between sequences.
| Property | Value |
|---|---|
| Category | Error Correction |
| Sub-category | Trellis Coded Modulation |
| Security status | 🎓 Educational Only |
| Complexity | Expert |
| Inventor | Gottfried Ungerboeck |
| Year | 1982 |
| Origin | 🇨🇭 Switzerland |
| Source | algorithms/ecc/trellis-coded-modulation.js |
Status: 🎓 Educational Only
| Issue | Description | Mitigation |
|---|---|---|
| Viterbi Complexity | Decoding complexity grows exponentially with number of trellis states. 4-state TCM is practical, but 64+ states become computationally intensive. | — |
| Channel Sensitivity | Performance depends on accurate channel estimation and soft-decision information. Hard-decision decoding significantly degrades performance. | — |
| Constellation Sensitivity | Set partitioning requires precise signal constellation mapping. Phase and amplitude errors degrade Euclidean distance properties. | — |
4 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.
Vector 1 — TCM 4-state 8-PSK: input 00 from state 0
| Field | Value |
|---|---|
input |
0000 |
expected |
000000 |
Vector 2 — TCM 4-state 8-PSK: input 01 from state 0
| Field | Value |
|---|---|
input |
0001 |
expected |
000001 |
Vector 3 — TCM 4-state 8-PSK: input 10 from state 0
| Field | Value |
|---|---|
input |
0100 |
expected |
010100 |
Vector 4 — TCM 4-state 8-PSK: input 11 from state 0
| Field | Value |
|---|---|
input |
0101 |
expected |
010101 |