TY - JOUR
T1 - Asymmetric Error Correction and Flash-Memory Rewriting Using Polar Codes
AU - En Gad, Eyal
AU - Li, Yue
AU - Kliewer, Jorg
AU - Langberg, Michael
AU - Jiang, Anxiao Andrew
AU - Bruck, Jehoshua
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/7
Y1 - 2016/7
N2 - 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.
AB - 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.
KW - Gelfand-Pinsker channel
KW - Polar codes
KW - writeonce-memory codes (WOMs)
UR - http://www.scopus.com/inward/record.url?scp=84976348987&partnerID=8YFLogxK
U2 - 10.1109/TIT.2016.2539967
DO - 10.1109/TIT.2016.2539967
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AN - SCOPUS:84976348987
SN - 0018-9448
VL - 62
SP - 4024
EP - 4038
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 7
M1 - 7429782
ER -