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 FilmusCommented Jun 27, 2017 at 20:04
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$\begingroup$ For large block the calculation is o(n^2) , is there more efficient way? $\endgroup$– Rorden JahneCommented Jun 28, 2017 at 17:34
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$\begingroup$ Perhaps it would be better if you explained what exactly you want to compute, including a complete formula. $\endgroup$– Yuval FilmusCommented Jun 28, 2017 at 17:36
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2 Answers
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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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read the paper "Designs of Bhattacharyya Parameter in the Construction of Polar Codes ". your answer is there.
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$\begingroup$ While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. $\endgroup$ Commented Aug 28, 2021 at 10:15