Channel Codes

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.

NKrateparity-check matrix
32111/3matrix
32161/2matrix
32222/3matrix
32243/4matrix
64221/3matrix
64321/2matrix
64432/3matrix
64483/4matrix
128431/3matrix
128641/2matrix
128862/3matrix
128963/4matrix
256861/3matrix
2561281/2matrix
2561712/3matrix
2561923/4matrix
5121711/3matrix
5122561/2matrix
5123422/3matrix
5123843/4matrix
10243421/3matrix
10245121/2matrix
10246832/3matrix
10247683/4matrix
20486831/3matrix
204810241/2matrix
204813662/3matrix
204815363/4

matrix

409613661/3matrix
409620481/2matrix
409627312/3matrix
409630723/4matrix
819227311/3matrix
819240961/2matrix
819254622/3matrix
819261443/4matrix
1638454621/3matrix
1638481921/2matrix
16384109232/3matrix
16384122883/4matrix

 

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.

 

 

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