On the Reed-Muller Rule Under Channel Polarization


C. Schnelling, A. Schmeink,


        Being the first provably capacity-achieving codes, polar codes present a constructive solution to a long-standing open problem in information theory. To achieve this elusive goal, that is, capacity on arbitrary symmetric binary-input discrete memoryless channels, their construction explicitly takes into account the statistics of the target channel. Code construction may be modeled as selecting a row space from a certain basis of Fn2. This is true for the much older class of Reed-Muller codes as well. In effect, the advent of polar codes reignited research on Reed-Muller codes. Recent results show that Reed-Muller codes are capacity-achieving on the binary erasure channel under maximum a-posteriori decoding. In this work, we assess how the row selections are related and conjecture that the Reed-Muller rule may provide a heuristic to select rows robust under successive cancellation decoding in the presence of varying channel conditions.

BibTEX Reference Entry 

	author = {Christopher Schnelling and Anke Schmeink},
	title = "On the Reed-Muller Rule Under Channel Polarization",
	pages = "341-346",
	booktitle = "2016 International Symposium on Wireless Communication Systems (ISWCS)",
	address = {Poznan, Poland},
	doi = 10.1109/ISWCS.2016.7600926,
	month = Sep,
	year = 2016,
	hsb = RWTH-2016-08268,


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