Polar Write Once Memory Codes
David Burshtein,Alona Strugatski +1 more
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TLDR
It is shown that the coding scheme achieves the capacity region of noiseless WOMs when an arbitrary number of multiple writes is permitted and the results can be generalized from binary to generalized WOMs, described by an arbitrary directed acyclic graph.Abstract:
A coding scheme for write once memory (WOM) using polar codes is presented. It is shown that the scheme achieves the capacity region of noiseless WOMs when an arbitrary number of multiple writes is permitted. The encoding and decoding complexities scale as O(N log N), where N is the blocklength. For N sufficiently large, the error probability decreases subexponentially in N. The results can be generalized from binary to generalized WOMs, described by an arbitrary directed acyclic graph, using nonbinary polar codes. In the derivation, we also obtain results on the typical distortion of polar codes for lossy source coding. Some simulation results with finite length codes are presented.read more
Citations
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Journal ArticleDOI
Improved Bounds on the Finite Length Scaling of Polar Codes
Dina Goldin,David Burshtein +1 more
TL;DR: Improved upper bounds on the blocklength required to communicate over binary-input channels using polar codes, below some given error probability, are derived and an improved bound on the number of non-polarizing channels is obtained.
Journal ArticleDOI
Achieving Marton’s Region for Broadcast Channels Using Polar Codes
TL;DR: This paper presents polar coding schemes for the two-user discrete memoryless broadcast channel (DM-BC) which achieve Marton’s region with both common and private messages, the best achievable rate region known to date.
Proceedings ArticleDOI
Achieving Marton's Region for Broadcast Channels Using Polar Codes
TL;DR: In this article, the authors proposed polar codes for the 2-user discrete memoryless broadcast channel (DM-BC) which achieved Marton's region with both common and private messages, and the proposed coding schemes possess the usual advantages of polar codes, i.e., they have low encoding and decoding complexity and a superpolynomial decay rate of the error probability.
Proceedings ArticleDOI
Write once, get 50% free: saving SSD erase costs using WOM codes
TL;DR: Reusable SSD is presented, in which invalid pages are reused for additional writes, without modifying the drive's exported storage capacity or page size, and the design achieves latency equivalent to a regular write.
Journal ArticleDOI
Capacity-Achieving Multiwrite WOM Codes
TL;DR: In this article, the authors gave an explicit construction of a family of capacity-achieving binary t-write WOM codes for any number of writes t, which have polynomial time encoding and decoding algorithms.
References
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Journal ArticleDOI
Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels
TL;DR: The paper proves that, given any B-DMC W with I(W) > 0 and any target rate R< I( W) there exists a sequence of polar codes {Cfrn;nges1} such that Cfrn has block-length N=2n, rate ges R, and probability of block error under successive cancellation decoding bounded as Pe(N,R) les O(N-1/4) independently of the code rate.
Proceedings ArticleDOI
List decoding of polar codes
Ido Tal,Alexander Vardy +1 more
TL;DR: It appears that the proposed list decoder bridges the gap between successive-cancellation and maximum-likelihood decoding of polar codes, and devise an efficient, numerically stable, implementation taking only O(L · n log n) time and O( L · n) space.
Proceedings ArticleDOI
On the rate of channel polarization
Erdal Arikan,Emre Telatar +1 more
TL;DR: It is shown that, for any binary-input discrete memoryless channel W with symmetric capacity I(W) and any rate R ≪I(W), the polar-coding block-error probability under successive cancellation decoding satisfies Pe (N, R) ≤ 2−Nβ for any β ≪ 1/2 when the block-length N is large enough.
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On the Rate of Channel Polarization
Erdal Arikan,Emre Telatar +1 more
TL;DR: In this paper, it was shown that for any binary-input discrete memoryless channel with symmetric capacity, the probability of block decoding error for polar coding under successive cancellation decoding satisfies O(P_e \le 2 √ n 2 −N^\beta) for any ε > 0 when the block length is large enough.
Proceedings ArticleDOI
Polarization for arbitrary discrete memoryless channels
TL;DR: In this article, it was shown that when the input alphabet size is a prime number, a similar construction to that for the binary case leads to polarization, and that all discrete memo-ryless channels can be polarized by randomized constructions.