FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3084582945> ?p ?o ?g. }

• W3084582945 endingPage "7332" @default.
• W3084582945 startingPage "7311" @default.
• W3084582945 abstract "Reed-Muller (RM) codes were introduced in 1954 and have long been conjectured to achieve Shannon's capacity on symmetric channels. The activity on this conjecture has recently been revived with the emergence of polar codes. RM codes and polar codes are generated by the same matrix G <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>m</sub> = [ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sup> <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>0</sup> ] <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>⊗m</sup> but using different subset of rows. RM codes 1 1 select simply rows having largest weights. Polar codes select instead rows having the largest conditional mutual information proceeding top to down in Gm; while this is a more elaborate and channel-dependent rule, the top-to-down ordering allows Arıkan to show that the conditional mutual information polarizes, and this gives directly a capacity-achieving code on any symmetric channel. RM codes are yet to be proved to have such a property, despite the recent success for the erasure channel. In this article, we connect RM codes to polarization theory. We show that proceeding in the RM code ordering, i.e., not top-to-down but from the lightest to the heaviest rows in <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>G</sub> m, the conditional mutual information again polarizes. Here “polarization” means that almost all the conditional mutual information becomes either very close to 0 or very close to 1. Polarization itself is a necessary condition for RM codes to achieve capacity on symmetric channels while polarization together with a strong order on the conditional mutual information gives a sufficient condition, where strong order means that rows with larger weight always correspond to larger conditional mutual information. Although we are not able to prove the strong order, we establish a partial order on the conditional mutual information, which is a subset of the strong order. While the main results of this article-polarization together with the partial order-provide some advances on the capacity-achieving conjecture of RM codes, we emphasize that our results do not allow us to prove the conjecture." @default.
• W3084582945 created "2020-09-21" @default.
• W3084582945 creator A5055776312 @default.
• W3084582945 creator A5061537073 @default.
• W3084582945 date "2020-12-01" @default.
• W3084582945 modified "2023-10-18" @default.
• W3084582945 title "Reed-Muller Codes Polarize" @default.
• W3084582945 cites W1529556207 @default.
• W3084582945 cites W1545614041 @default.
• W3084582945 cites W1978526953 @default.
• W3084582945 cites W2004229705 @default.
• W3084582945 cites W2034946612 @default.
• W3084582945 cites W2055534149 @default.
• W3084582945 cites W2080479164 @default.
• W3084582945 cites W2103524940 @default.
• W3084582945 cites W2103749128 @default.
• W3084582945 cites W2106045225 @default.
• W3084582945 cites W2112446888 @default.
• W3084582945 cites W2121417875 @default.
• W3084582945 cites W2122726380 @default.
• W3084582945 cites W2131457481 @default.
• W3084582945 cites W2136370860 @default.
• W3084582945 cites W2150498905 @default.
• W3084582945 cites W2162746978 @default.
• W3084582945 cites W2164368671 @default.
• W3084582945 cites W2570893422 @default.
• W3084582945 cites W2589095445 @default.
• W3084582945 cites W2591190829 @default.
• W3084582945 cites W2963024133 @default.
• W3084582945 cites W2963689158 @default.
• W3084582945 cites W2963710189 @default.
• W3084582945 cites W2963852187 @default.
• W3084582945 cites W2964292940 @default.
• W3084582945 cites W2964317445 @default.
• W3084582945 cites W2971934663 @default.
• W3084582945 cites W2976297103 @default.
• W3084582945 cites W3001795748 @default.
• W3084582945 cites W3102122722 @default.
• W3084582945 doi "https://doi.org/10.1109/tit.2020.3023487" @default.
• W3084582945 hasPublicationYear "2020" @default.
• W3084582945 type Work @default.
• W3084582945 sameAs 3084582945 @default.
• W3084582945 citedByCount "23" @default.
• W3084582945 countsByYear W30845829452019 @default.
• W3084582945 countsByYear W30845829452020 @default.
• W3084582945 countsByYear W30845829452021 @default.
• W3084582945 countsByYear W30845829452022 @default.
• W3084582945 countsByYear W30845829452023 @default.
• W3084582945 crossrefType "journal-article" @default.
• W3084582945 hasAuthorship W3084582945A5055776312 @default.
• W3084582945 hasAuthorship W3084582945A5061537073 @default.
• W3084582945 hasBestOaLocation W30845829451 @default.
• W3084582945 hasConcept C11413529 @default.
• W3084582945 hasConcept C114614502 @default.
• W3084582945 hasConcept C118615104 @default.
• W3084582945 hasConcept C135598885 @default.
• W3084582945 hasConcept C177264268 @default.
• W3084582945 hasConcept C199360897 @default.
• W3084582945 hasConcept C2776760102 @default.
• W3084582945 hasConcept C2780990831 @default.
• W3084582945 hasConcept C33923547 @default.
• W3084582945 hasConcept C41008148 @default.
• W3084582945 hasConceptScore W3084582945C11413529 @default.
• W3084582945 hasConceptScore W3084582945C114614502 @default.
• W3084582945 hasConceptScore W3084582945C118615104 @default.
• W3084582945 hasConceptScore W3084582945C135598885 @default.
• W3084582945 hasConceptScore W3084582945C177264268 @default.
• W3084582945 hasConceptScore W3084582945C199360897 @default.
• W3084582945 hasConceptScore W3084582945C2776760102 @default.
• W3084582945 hasConceptScore W3084582945C2780990831 @default.
• W3084582945 hasConceptScore W3084582945C33923547 @default.
• W3084582945 hasConceptScore W3084582945C41008148 @default.
• W3084582945 hasFunder F4320309327 @default.
• W3084582945 hasFunder F4320337387 @default.
• W3084582945 hasIssue "12" @default.
• W3084582945 hasLocation W30845829451 @default.
• W3084582945 hasLocation W30845829452 @default.
• W3084582945 hasOpenAccess W3084582945 @default.
• W3084582945 hasPrimaryLocation W30845829451 @default.
• W3084582945 hasRelatedWork W1529715114 @default.
• W3084582945 hasRelatedWork W1978042415 @default.
• W3084582945 hasRelatedWork W2120826334 @default.
• W3084582945 hasRelatedWork W2740334431 @default.
• W3084582945 hasRelatedWork W2951211509 @default.
• W3084582945 hasRelatedWork W3038654277 @default.
• W3084582945 hasRelatedWork W3119737209 @default.
• W3084582945 hasRelatedWork W4212808623 @default.
• W3084582945 hasRelatedWork W4225848310 @default.
• W3084582945 hasRelatedWork W4301927665 @default.
• W3084582945 hasVolume "66" @default.
• W3084582945 isParatext "false" @default.
• W3084582945 isRetracted "false" @default.
• W3084582945 magId "3084582945" @default.
• W3084582945 workType "article" @default.