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Polar-code construction and decoding techniques

Amiridi Magda

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Summary

Polar codes, recently invented by Arikan, are the first provably capacity achieving codes for any binary input symmetric discrete memoryless channelwith low encoding and decoding complexity. This thesis explores the practicalimplementation of polar codes which are complexity efficient and performwell for binary erasure channel (BEC) and binary symmetric channel (BSC).The explicit code construction is based on a characteristic called channel polarization which involves generating N extremal (perfect or completely noisy)channels from N independent uses of the same base channel. Informationbits are sent over the noiseless channels while pilot bits, called frozen bits,are assigned to the noisy ones. Code design for BEC is based on the recursiverelations presented in the original paper whereas for BSC we propose aheuristic and efficient algorithm and compare it to the method of recursiveestimation of Bhattacharyya parameters of bit-channels. The encoding is implemented using a recursive butterfly structure with O(N logN) complexity,where N is the block length of the code. Two main low complexity decodersare compared in terms of bit error rate: successive cancellation decoder proposed by Arikan having complexity O(N logN) with susceptibility to errorpropagation and mediocre bit error rate performance at small or moderatecode lengths and list decoder, proposed by Tal and Vardy, with complexityO(LN logN) where L is the list size.

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