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• W2893525661 abstract "We prove that, at least for the binary erasure channel, the polar-coding paradigm gives rise to codes that not only approach the Shannon limit but, in fact, do so under the best possible scaling of their block length as a function of the gap to capacity. This result exhibits the first known family of binary codes that attain both optimal scaling and quasi-linear complexity of encoding and decoding. Specifically, for any fixed $delta gt 0$, we exhibit binary linear codes that ensure reliable communication at rates within $epsilon gt 0$ of capacity with block length $n = O(1/epsilon^{2+delta})$, construction complexity $Theta(n)$, and encoding/decoding complexity $Theta(nlog n)$." @default.
• W2893525661 created "2018-10-05" @default.
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• W2893525661 date "2018-11-01" @default.
• W2893525661 modified "2023-10-18" @default.
• W2893525661 title "Binary Linear Codes with Optimal Scaling: Polar Codes with Large Kernels" @default.
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• W2893525661 doi "https://doi.org/10.1109/itw.2018.8613428" @default.
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