Polar Codes: Robustness of the Successive Cancellation Decoder with Respect to Quantization

Polar codes provably achieve the capacity of a wide array of channels under successive decoding. This assumes infinite precision arithmetic. Given the successive nature of the decoding algorithm, one might worry about the sensitivity of the performance to the precision of the computation. We show that even very coarsely quantized decoding algorithms lead to excellent performance. More concretely, we show that under successive decoding with an alphabet of cardinality only three, the decoder still has a threshold and this threshold is a sizable fraction of capacity. More generally, we show that if we are willing to transmit at a rate delta below capacity, then we need only c log(1/delta) bits of precision, where c is a universal constant.


Published in:
2012 IEEE International Symposium On Information Theory Proceedings (Isit), 1962-1966
Presented at:
IEEE International Symposium on Information Theory, Cambridge, MA, 1-6 July 2012
Year:
2012
Publisher:
New York, Ieee
ISBN:
978-1-4673-2579-0
Laboratories:




 Record created 2013-04-05, last modified 2018-03-17


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