Towards Practical Length-compatible Polar Codes
Author | : Adam Cavatassi |
Publisher | : |
Total Pages | : |
Release | : 2019 |
ISBN-10 | : OCLC:1117497955 |
ISBN-13 | : |
Rating | : 4/5 (55 Downloads) |
Book excerpt: "In 2008, a new class of block error correction codes, known as polar codes, were provenby Erdal Arıkan to be able to achieve the Shannon limit. Through inventive new de-coding algorithms and fast code constructions, polar codes have become an attractivehigh-performance error correction code for practical use. These innovations have resultedin adoption of polar codes in the upcoming 3GPP 5 th generation standard for New Ra-dio. Still, polar codes are hindered by certain inflexible characteristics. Arıkan's originalpolar code definition limits block lengths to powers of two, due to a recursive Kroneckerproduct of the 2 × 2 polarizing kernel. This constraint presents a considerable obstacle,as many realistic scenarios call for all code lengths to be readily available. Rate-matchingtechniques, known as puncturing and shortening, allow for flexible polar code lengths,albeit with inefficient decoding complexity. Multi-kernel polar codes produce native codelengths that are powers of two and/or three with the addition of a 3 × 3 ternary kernel,although they necessitate specialized decoders and code design. This thesis will exploreand propose techniques that are intended for maximizing the flexibility and efficiencyof polar codes, as well as analyze any trade-offs affecting error correction performance.An in-depth study is presented that compares state-of-the-art length-flexible polar codeswith the 3GPP standardized polar codes. This inquiry finds that the 5G standard offersa highly simplified polar code construction with minimal loss to error correction per-formance. Further, multi-kernel polar codes were found to have a negative correlationbetween error correction performance and the quantity of ternary Kronecker constituents.This thesis also proposes a new fast successive cancellation decoder that is compliant withmulti-kernel polar codes. The ternary kernel is further investigated by testing its rate-matching and systematic properties. Finally, this thesis proposes a new scheme calledasymmetric polar codes. We present details on generator matrix definition, informa-tion set design, and decoding schedules, as well as perform comparisons with competingschemes using simulations and a comprehensive analysis. Asymmetric polar codes offerflexible block lengths with decoding complexity lower than equivalent length-compatiblepolar codes under successive cancellation. The enclosed findings indicate that asymmetricpolar codes afford comparable error correction performance to the competing schemes,while dividing the number of successive cancellation decoding operations by up to a fac-tor of two. The thesis is then concluded by recommending appropriate extensions of thiswork for future research." --