Asymmetric Error Correction and Flash-Memory Rewriting Using Polar Codes

Eyal En Gad, Yue Li, Jorg Kliewer, Michael Langberg, Anxiao Andrew Jiang, Jehoshua Bruck

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We propose efficient coding schemes for two communication settings: 1) asymmetric channels and 2) channels with an informed encoder. These settings are important in non-volatile memories, as well as optical and broadcast communication. The schemes are based on non-linear polar codes, and they build on and improve recent work on these settings. In asymmetric channels, we tackle the exponential storage requirement of previously known schemes that resulted from the use of large Boolean functions. We propose an improved scheme that achieves the capacity of asymmetric channels with polynomial computational complexity and storage requirement. The proposed non-linear scheme is then generalized to the setting of channel coding with an informed encoder using a multicoding technique. We consider specific instances of the scheme for flash memories that incorporate error-correction capabilities together with rewriting. Since the considered codes are non-linear, they eliminate the requirement of previously known schemes (called polar write-once-memory codes) for shared randomness between the encoder and the decoder. Finally, we mention that the multicoding scheme is also useful for broadcast communication in Marton's region, improving upon previous schemes for this setting.

Original languageEnglish (US)
Article number7429782
Pages (from-to)4024-4038
Number of pages15
JournalIEEE Transactions on Information Theory
Volume62
Issue number7
DOIs
StatePublished - Jul 2016

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

Keywords

  • Gelfand-Pinsker channel
  • Polar codes
  • writeonce-memory codes (WOMs)

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