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Polar codes are the first provably capacity-achieving forward errorcorrection codes. To improve decoder throughput, the symbol-decision SCalgorithm makes hard-decision for multiple bits at a time. In this paper, weprove that for polar codes, the symbol-decision SC algorithm is better than thebit-decision SC algorithm in terms of the frame error rate (FER) performancebecause the symbol-decision SC algorithm performs a local maximum likelihooddecoding within a symbol. Moreover, the bigger the symbol size, the better theFER performance. Finally, simulation results over both the additive whiteGaussian noise channel and the binary erasure channel confirm our theoreticalanalysis.

Error Performance Analysis of the Symbol-Decision SC Polar Decoder