Polar Codes: 2D Polarization and Decoding

Polar code

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Code length N = 2^n, n

Code rate R

Eb/N0

Readouts

N / K (info bits)

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Measured BER at Eb/N0

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Frame error rate

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Uncoded BPSK BER

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Mean capacity of info set

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Frames simulated

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BEC polarization: Z(W-) = 2Z - Z^2, Z(W+) = Z^2 (Arikan 2009), designed at erasure 1-R. Info bits go on the K best synthetic channels, rest frozen to 0. Decoder: successive cancellation (min-sum f, g updates) over BPSK/AWGN.