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Information bit selection in polar coding for the binary symmetric channel

Bountrogiannis Konstantinos

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Summary

Polar codes is a new scheme of channel coding, which is the first provably capacity-achieving coding scheme for a wide class of channels, the binary discrete memoryless channels. At the same time, they use low complexity encoding and decoding algorithms, which makes them attractive for a wide range of use-cases. These algorithms scale as O(NlogN), where N is the blocklength of the code. Polar codes exploit channel polarization, a very common phenomenon which arises when one takes N independent copies of a channel and transforms them into another set of N channels. Under channel polarization, the channels are converted to a set of extremal (either perfect or completely noisy) channels, called bit-channels. In the presence of channel polarization, the information vector is sent through the perfect bit-channels, while a fixed vector of arbitrary bits is sent through the useless bit-channels. A problem which arises is the determination of which bit-channels are perfect and which are useless. This problem, called the “construction of polar codes” among researchers, has been addressed successfully and efficiently only for the binary erasure channel (BEC). The non-universality property of polar codes complicates their construction, because the behaviour of a bit-channel may be perfect for one physical channel but noisy for another. The adoption of polar codes in 5G NR strengthens the demand for a fast and adaptive construction scheme. This thesis attempts to design an efficient algorithm for the construction of polar codes for the binary symmetric channel (BSC), taking advantage of proved universal partial orders among the bit-channels and state-of-the-art algorithms which approximate efficiently upper and lower bounds of the probability of error of the bit-channels. The simulation results show a marginal time-running difference over the explicit use of the approximation algorithms, which can be used computationally for a more accurate construction.

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