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In polar codes, the frozen bits in each message are determined through the worst channel, where the relevant parameter is the Bhattacharyya .

How can I estimate Bhattacharyya parameter for BSC channel?

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  • $\begingroup$ There is no need to estimate. You can compute it exactly using the formula. See for example formula (14) on page 5 of this paper. $\endgroup$ – Yuval Filmus Jun 27 '17 at 20:04
  • $\begingroup$ For large block the calculation is o(n^2) , is there more efficient way? $\endgroup$ – Rorden Jahne Jun 28 '17 at 17:34
  • $\begingroup$ Perhaps it would be better if you explained what exactly you want to compute, including a complete formula. $\endgroup$ – Yuval Filmus Jun 28 '17 at 17:36
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I do not think you can use formula (14) on page 5 of 'How to construct polar codes'. I think you want to compute Bhattacharyya parameters after channel polarization. Hence, you need to compute transition probabilities of synthesized channels firstly, and then compute Bhattacharyya parameters using formula (14) on page 5 of 'How to construct polar codes'. The formula of transition probabilities of synthesized channels is give by Arikan in his TIT paper, but it is not easy to implement it.

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