First capacity-achieving codes with explicit construction. Provably achieve Shannon channel capacity for symmetric binary-input discrete memoryless channels. Adopted in 5G NR for control channels (PBCH, PDCCH, PUCCH). Based on channel polarization phenomenon where independent copies of a channel are combined to produce extremal channels. Successive cancellation decoding provides efficient implementation.
| Property | Value |
|---|---|
| Category | Error Correction |
| Sub-category | Linear Code |
| Security status | π Educational Only |
| Complexity | Expert |
| Inventor | Erdal ArΔ±kan |
| Year | 2008 |
| Origin | π International |
| Source | algorithms/ecc/polar-code.js |
Status: π Educational Only
| Issue | Description | Mitigation |
|---|---|---|
| Finite-Length Performance | Polar codes require large blocklengths to approach capacity; short blocklengths show performance gap | β |
| Decoding Latency | Successive cancellation decoding is inherently sequential, leading to higher latency compared to parallel decoders | β |
| Construction Complexity | Optimal frozen bit selection requires channel knowledge and complex construction algorithms | β |
5 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.
Vector 1 β Polar (8,4) all-zero codeword
| Field | Value |
|---|---|
input |
00000000 |
expected |
0000000000000000 |
Vector 2 β Polar (8,4) all-one codeword from single info bit
| Field | Value |
|---|---|
input |
00000001 |
expected |
0101010101010101 |
Vector 3 β Polar (8,4) single info bit at position 3
| Field | Value |
|---|---|
input |
01000000 |
expected |
0100010001000100 |
Vector 4 β Polar (8,4) single info bit at position 5
| Field | Value |
|---|---|
input |
00010000 |
expected |
0101000001010000 |
Vector 5 β Polar (8,4) two info bits pattern
| Field | Value |
|---|---|
input |
01000001 |
expected |
0001000100010001 |