Polar Codes
All polar codes [1] used on this page are optimized for the AWGN channel with a signal-to-noise ratio of 3.0 dB per channel symbol. The codes are constructed using the improved degrading-merge algorithm (Algorithm D in [2]) with parameters μ=128 (μ=2000 for the channel).
The table contains polar codes of length 2^n for n={5,...,14}, using target rates {1/2, 1/3, 2/3, 3/4}. Note that the actual rates are slightly higher in some cases. In addition, the positions of the frozen indices for the rate-1/3 codes are listed in this file. The indices are ordered by increasing error probability of the according bit-channel (see [1] and [2] for details); hence, the frozen indices for the higher-rate codes can be obtained by removing the appropriate number of indices from the beginning of the respective list.
N | K | rate | parity-check matrix |
---|---|---|---|
32 | 11 | 1/3 | matrix |
32 | 16 | 1/2 | matrix |
32 | 22 | 2/3 | matrix |
32 | 24 | 3/4 | matrix |
64 | 22 | 1/3 | matrix |
64 | 32 | 1/2 | matrix |
64 | 43 | 2/3 | matrix |
64 | 48 | 3/4 | matrix |
128 | 43 | 1/3 | matrix |
128 | 64 | 1/2 | matrix |
128 | 86 | 2/3 | matrix |
128 | 96 | 3/4 | matrix |
256 | 86 | 1/3 | matrix |
256 | 128 | 1/2 | matrix |
256 | 171 | 2/3 | matrix |
256 | 192 | 3/4 | matrix |
512 | 171 | 1/3 | matrix |
512 | 256 | 1/2 | matrix |
512 | 342 | 2/3 | matrix |
512 | 384 | 3/4 | matrix |
1024 | 342 | 1/3 | matrix |
1024 | 512 | 1/2 | matrix |
1024 | 683 | 2/3 | matrix |
1024 | 768 | 3/4 | matrix |
2048 | 683 | 1/3 | matrix |
2048 | 1024 | 1/2 | matrix |
2048 | 1366 | 2/3 | matrix |
2048 | 1536 | 3/4 | |
4096 | 1366 | 1/3 | matrix |
4096 | 2048 | 1/2 | matrix |
4096 | 2731 | 2/3 | matrix |
4096 | 3072 | 3/4 | matrix |
8192 | 2731 | 1/3 | matrix |
8192 | 4096 | 1/2 | matrix |
8192 | 5462 | 2/3 | matrix |
8192 | 6144 | 3/4 | matrix |
16384 | 5462 | 1/3 | matrix |
16384 | 8192 | 1/2 | matrix |
16384 | 10923 | 2/3 | matrix |
16384 | 12288 | 3/4 | matrix |
Literature
[1] Arιkan, E.: Channel polarization: a method for constructing capacity-achieving codes for symmetric binary-input memoryless channels. IEEE Transactions on Information Theory, vol. 55, 2009, pp. 3051–3073.
[2] Tal, I. & Vardy, A: How to Construct Polar Codes. IEEE Transactions on Information Theory, vol. 59, 2013, pp. 6562-6582.