Capacity-Achieving Polar Codes for Arbitrarily Permuted Parallel Channels

Hof, Eran; Sason, Igal; Shamai, Shlomo; Tian, Chao

doi:10.1109/tit.2012.2236971

Cited by 14 publications

(7 citation statements)

References 16 publications

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“…Note that decoding a random code, as in the proof of Lemma 3, still involves a complexity that is only polynomial in M . However, more practical capacity-achieving code families for the K-parallel multi-draw channel might be obtained by [25]'s rate-matching codes or [26]'s polar code construction.…”

Section: B Lemmasmentioning

confidence: 99%

Achievable Rates of Concatenated Codes in DNA Storage under Substitution Errors

Lenz¹,

Welter²,

Puchinger³

2020

Preprint

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In this paper, we study achievable rates of concatenated coding schemes over a deoxyribonucleic acid (DNA) storage channel. Our channel model incorporates the main features of DNA-based data storage. First, information is stored on many, short DNA strands. Second, the strands are stored in an unordered fashion inside the storage medium and each strand is replicated many times. Third, the data is accessed in an uncontrollable manner, i.e., random strands are drawn from the medium and received, possibly with errors. As one of our results, we show that there is a significant gap between the channel capacity and the achievable rate of a standard concatenated code in which one strand corresponds to an inner block. This is in fact surprising as for other channels, such as q-ary symmetric channels, concatenated codes are known to achieve the capacity. We further propose a modified concatenated coding scheme by combining several strands into one inner block, which allows to narrow the gap and achieve rates that are close to the capacity.

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Section: B Lemmasmentioning

confidence: 99%

Achievable Rates of Concatenated Codes in DNA Storage under Substitution Errors

Lenz¹,

Welter²,

Puchinger³

2020

Preprint

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“…condition, into the non-identically distributed DMC case. This extension was performed in previous literatures, in the names of "parallel channels" [7,8] and "non-stationary channels" [3] with the measure of the symmetric capacity.…”

Section: Lemma 1 Suppose Wmentioning

confidence: 99%

“…In previous studies, [8] and [3], it is assumed that the characteristics of underlying discrete memoryless channels are fully exposed to the transceiver; thus, the encoder and the decoder exploit this information. Under this condition, it is proved that polar codes can achieve the symmetric capacity.…”

Section: Non-identical Binary Erasure Channels With Random Erasure Prmentioning

confidence: 99%

“…The question then arises about whether the parallel channel capacity is achievable via polar codes. In [7,8], it is demonstrated, under a non-identically distributed channel assumption, that when all channel parameters (CP) are given to the transceiver, polar codes can achieve the capacity in both degraded and non-degraded channel settings.…”

Section: Introductionmentioning

confidence: 99%

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Polar codes for non-identically distributed channels

Kim

Lee

2016

J Wireless Com Network

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We introduce new polar coding schemes for independent non-identically distributed parallel binary discrete memoryless channels. The first scheme is developed for the case where underlying channels are time invariant (the case of a deterministic channel parameters), while the other schemes deal with a scenario where underlying channels change based on a distribution (the case of random channel parameters). For the former case, we also discuss the importance of the usage of an interleaver Q to enhance system reliability, and for the latter case, we model the channel behavior of binary erasure channels. It is shown that the proposed polar coding schemes achieve a symmetric capacity.

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“…for C l,u as defined in (9), and for some u ∈ F v 2 . Furthermore, define C(n) ⊆ F n 2 × F n 2 as C(n) := C 1 (n) ∪ C 2 (n).…”

Section: Lower Bounds From Non-linear Code Constructionsmentioning

confidence: 99%

Asymmetric Lee distance codes for DNA-based storage

Gabrys

Kiah

Milenković

2015

2015 IEEE International Symposium on Information Theory (ISIT)

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We introduce a new family of codes, termed asymmetric Lee distance (ALD) codes, designed to correct errors arising in DNA-based storage systems and systems with parallel string transmission protocols. ALD codes are defined over a quaternary alphabet and analyzed in this particular setting, but the derived results hold for other alphabet sizes as well. Our technical contributions are twofold: First, we derive upper bounds on the size of the codes under the ALD metric based on linear programming techniques. Second, we propose a number of code constructions which imply lower bounds.

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Capacity-Achieving Polar Codes for Arbitrarily Permuted Parallel Channels

Abstract: Channel coding over arbitrarily-permuted parallel channels was first studied by Willems et al. (2008). This paper introduces capacity-achieving polar coding schemes for arbitrarily-permuted parallel channels where the component channels are memoryless, binary-input and output-symmetric.

Cited by 14 publications

References 16 publications

Achievable Rates of Concatenated Codes in DNA Storage under Substitution Errors

Achievable Rates of Concatenated Codes in DNA Storage under Substitution Errors

Polar codes for non-identically distributed channels

Asymmetric Lee distance codes for DNA-based storage

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