Summary
The 2018 International Symposium on Information Theory and Its Applications　(ISITA2018)
2018
Session Number:Tu-PM-2-1
Session:
Number:Tu-PM-2-1.2
On the Properties of Bit-Reversal Shortening in Polar Codes
Prakash Chaki, Norifumi Kamiya,
pp.437-441
Publication Date:2018/10/18
Online ISSN:2188-5079
DOI:10.34385/proc.55.Tu-PM-2-1.2
PDF download
Summary:
Puncturing and shortening are widely used methods employed to design arbitrary rate codes from a mother code of given rate. In the context of polar codes, the encoding process has to be completely redone based on the codelength and coding rate for any given shortening/puncturing pattern which makes the implementation of a rate-compatible polar code system very complex. This happens as reliability ordering of the polarized bitchannels gets altered post shortening/puncturing; thus making it necessary to recompute the bit-channel reliabilities tailored to the new reduced codelength followed by sorting them again (in other words, a complete reconstruction). It has been noted before that a bit reversal shortening (BRS) scheme has a special property: it does not require the said reordering of bit-channels, which makes the encoder implementation significantly simple and pragmatic. While this property is extremely intriguing both theoretically and practically, no detailed study on this subject is available in literature. In this paper, we show the relation of BRS with prior art, highlight the said property across wide range of code parameters and then delve deep into what leads up to that property. We observe that like all other schemes, BRS also changes the reliability order of indices, but in a very localized manner. Consequently, the non-frozen set for bit-reverse shortened polar code is nearly same as that of the mother code. Extensive simulation of polar codes is provided to validate the findings.