Polar Codes' Simplicity, Random Codes' Durability

12/19/2019 ∙ by Hsin-Po Wang, et al. ∙ 0

Over any discrete memoryless channel, we build codes such that: for one, their block error probabilities and code rates scale like random codes'; and for two, their encoding and decoding complexities scale like polar codes'. Quantitatively, for any constants π,ρ>0 such that π+2ρ<1, we construct a sequence of error correction codes with block length N approaching infinity, block error probability (-N^π), code rate N^-ρ less than the Shannon capacity, and encoding and decoding complexity O(Nlog N) per code block. The putative codes take uniform ς-ary messages for sender's choice of prime ς. The putative codes are optimal in the following manner: Should π+2ρ>1, no such codes exist for generic channels regardless of alphabet and complexity.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 40

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.