Explicit constructions of finite-length WOM codes

Chee, Yeow Meng; Kiah, Han Mao; Vard, Alexander; Yaakobi, Eitan

doi:10.1109/isit.2017.8007052

Cited by 7 publications

(4 citation statements)

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“…Each information word will be identified by a codeset, the codeword taken from the appropriate codeset should have ones on all positions where the memory has ones and hence the ones in complement of the codeword should have empty intersection with the ones of the memory. As was mentioned, this application to WOM codes was considered in [5]. We believe that other applications will arise in the future.…”

Section: Introductionmentioning

confidence: 95%

“…Specifically, an Earlier results of this paper were presented at the 2018 Proceedings of the IEEE ISIT [4]. which are very important in coding for flash memories (see [5] and references therein). This application of codesets into construction of WOM codes was written in detail in [5] and is described in short as follows.…”

Section: Introductionmentioning

confidence: 99%

“…Our main target in this paper are cooling codes, but these codes, or more precisely their definition by codesets, might have other applications too. One such application is in the design of WOM (Once Write Memory) codes which are very important in coding for flash memories (see [5] and references therein). This application of codesets into construction of WOM codes was written in detail in [5] and is described in short as follows.…”

Section: Introductionmentioning

confidence: 99%

“…One such application is in the design of WOM (Once Write Memory) codes which are very important in coding for flash memories (see [5] and references therein). This application of codesets into construction of WOM codes was written in detail in [5] and is described in short as follows. In a WOM code one is trying to write binary information words of length k into a memory of length n, where the information is written only in positions where there are zeroes.…”

Section: Introductionmentioning

confidence: 99%

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Low-Power Cooling Codes with Efficient Encoding and Decoding

Chee

Etzion

Kiah

et al. 2018

2018 IEEE International Symposium on Information Theory (ISIT)

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A class of low-power cooling (LPC) codes, to control simultaneously both the peak temperature and the average power consumption of interconnects, was introduced recently. An (n, t, w)-LPC code is a coding scheme over n wires that (A) avoids state transitions on the t hottest wires (cooling), and (B) limits the number of transitions to w in each transmission (low-power).A few constructions for large LPC codes that have efficient encoding and decoding schemes, are given. In particular, when w is fixed, we construct LPC codes of size (n/w) w−1 and show that these LPC codes can be modified to correct errors efficiently. We further present a construction for large LPC codes based on a mapping from cooling codes to LPC codes. The efficiency of the encoding/decoding for the constructed LPC codes depends on the efficiency of the decoding/encoding for the related cooling codes and the ones for the mapping.(n, t, w)-LPC code is a coding scheme for communication over a bus consisting of n wires, if the scheme has the following two features:(A) every transmission does not cause state transitions on the t hottest wires;(B) the number of state transitions on all the wires is at most w in every transmission. LPC codes have both features, while cooling codes control only the peak temperature.Definition 1. For n and t, an (n, t)-cooling code C of size M is defined as a collection {C 1 , C 2 , . . . , C M }, where C 1 , C 2 , . . . , C M are disjoint subsets of {0, 1} n satisfying the following property: for any set S ⊆ [n] of size |S| = t and for i ∈ [M], there exists a vector u ∈ C i such that supp(u) ∩ S = ∅. We refer to C 1 , C 2 , . . . , C M as codesets and the vectors in them as codewords.Using partial spreads, Chee et al. [3] constructed LPC codes with efficient encoding and decoding schemes.When t ≤ 0.687n and w ≥ (n − t)/2, these codes achieve optimal asymptotic rates. However, when w is small, i.e. low-power coding is used, the code rates are small and Chee et al. proposed another construction based on decomposition of the complete hypergraph into perfect matchings. While the construction results in LPC codes of large size, usually efficient encoding and decoding algorithms are not known.In this work, we focus on this regime (w small) and construct LPC codes with efficient encoding and decoding schemes. Specifically, our contributions are as follows.(I) We propose a method that takes a linear erasure code as input and constructs an LPC code. Using this method, we then construct a family of LPC codes of size (n/w) w−1 which attains the asymptotic upper bound O(n w−1 ) when w is fixed. We also use this method to construct a class of LPC codes of size (n/w) w−e−1 which is able to correct e transmission errors.(II) We propose efficient encoding/decoding schemes for the LPC codes of the given construction. In particular, for the above family of LPC codes, we demonstrate encoding with O(n) multiplications over F q and decoding with O(w 3 ) multiplications over F q , where q = n/w. Furthermore, the related class of LPC codes i...

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Section: Introductionmentioning

confidence: 95%