ITW Dublin : historical take on polar codes

I am at ITW in Dublin, and I will write a short post or two about it. I missed most of the conference until now due to jetlag and late arrival, but I did make it to Arikan’s plenary lecture this morning on the historical context for polar codes. It was a really nice talk about successive decoding and how it relates to polar codes. A central issue is the computation cutoff rate R_{comp}, which prevents successive decoding from reaching capacity.

He described Pinsker’s “concatenated” construction of convolutional encoders around a block code, which is capacity-achieving but inefficient, and Massey’s 1981 construction of codes for the quaternary erasure channel which decomposes the QEC into two parallel BECs whose noise is correlated (you just relabel the 4 inputs with 2 bits and treat the two bits as going through parallel BECs). This is efficient, increases R_{comp}, but is not enough to get to capacity. However, in a sense, Massey’s construction is like doing one step in polar codes, and combining this with Pinkser’s ideas starts getting the flavor of the channel polarization effect.

Good stuff!

One thought on “ITW Dublin : historical take on polar codes

  1. Pingback: Emmanuel Abbe: Erdal Arıkan’s Polar Codes | Combinatorics and more

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