LDPC codes constructed from small prototype graphs (protographs) expanded via copy-and-permute operations. AR4JA (Accumulate-Repeat-4-Jagged-Accumulate) protograph provides near-capacity performance with structured design enabling analytical threshold analysis. Adopted in NASA deep space communications (CCSDS standard), DVB-S2X satellite broadcasting, and 5G NR. Educational implementation demonstrates protograph expansion with circulant permutation matrices.
| Property | Value |
|---|---|
| Category | Error Correction |
| Sub-category | Structured LDPC Code |
| Security status | 🎓 Educational Only |
| Complexity | Expert |
| Inventor | Dariush Divsalar, Sam Dolinar, Christopher Jones |
| Year | 2004 |
| Origin | 🇺🇸 United States |
| Source | algorithms/ecc/protograph-ldpc.js |
Status: 🎓 Educational Only
| Issue | Description | Mitigation |
|---|---|---|
| Iterative Decoding Complexity | Belief propagation decoder requires multiple iterations with high computational cost | — |
| Short Cycle Impact | Small protographs expanded with small lifting factors can create short cycles degrading performance | — |
| Error Floor Phenomenon | Trapping sets in expanded graph can cause performance degradation at low error rates | — |
4 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.
Vector 1 — Protograph LDPC all-zero codeword (N=4)
| Field | Value |
|---|---|
input |
0000000000000000 |
expected |
00000000000000000000000000000000 |
Vector 2 — Protograph LDPC round-trip test 1
| Field | Value |
|---|---|
input |
0100010001000100 |
expected |
(empty) |
Vector 3 — Protograph LDPC round-trip test 2
| Field | Value |
|---|---|
input |
0001000100010001 |
expected |
(empty) |
Vector 4 — Protograph LDPC round-trip test 3
| Field | Value |
|---|---|
input |
0101000001010000 |
expected |
(empty) |