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• W2112446888 abstract "We explore the relationship between polar and RM codes and we describe a coding scheme which improves upon the performance of the standard polar code at practical block lengths. Our starting point is the experimental observation that RM codes have a smaller error probability than polar codes under MAP decoding. This motivates us to introduce a family of codes that “interpolates” between RM and polar codes, call this family C <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>inter</sub> = {C <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>α</sub> : α ∈ [0, 1j}, where C <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>α|α=1</sub> is the original polar code, and C <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>α|α=0</sub> is an RM code. Based on numerical observations, we remark that the error probability under MAP decoding is an increasing function of α. MAP decoding has in general exponential complexity, but empirically the performance of polar codes at finite block lengths is boosted by moving along the family Cinter even under low-complexity decoding schemes such as, for instance, belief propagation or successive cancellation list decoder. We demonstrate the performance gain via numerical simulations for transmission over the erasure channel as well as the Gaussian channel." @default.
• W2112446888 created "2016-06-24" @default.
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• W2112446888 creator A5061114394 @default.
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• W2112446888 date "2014-09-01" @default.
• W2112446888 modified "2023-10-01" @default.
• W2112446888 title "From Polar to Reed-Muller Codes: A Technique to Improve the Finite-Length Performance" @default.
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• W2112446888 doi "https://doi.org/10.1109/tcomm.2014.2345069" @default.
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