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low-complexity Rate- and Channel-Configurable Concatenated codes

JOURNAL OF LIGHTWAVE TECHNOLOGY 2021年第7期39卷 1976-1983页

作者： Barakatain, Masoud Kschischang, Frank R. Univ Toronto Edward S Rogers Sr Dept Elect & Comp Engn Toronto ON M5S 3G4 Canada

A low-complexity rate- and channel-configurable forward error-correction (FEC) scheme is proposed, consisting of an inner low-density parity-check code concatenated with an outer zipper code. A tool is developed to optimize a multi-level code architecture so that it can operate at multiple transmission rates, channel qualities, and modulation orders. The optimization criterion is selected to maintain a low estimated data-flow in its decoding operation. A hardware-friendly quasi-cyclic structure is considered for the inner code and the performance and complexity is reported for various designed FEC configurations. Compared to existing FEC schemes, the proposed designs deliver a similar performance with up to 63% reduction in decoding complexity or provide up to 0.6 dB coding gain at a similar decoding complexity.

关键词： Channel-adaptivity concatenated coding low-complexity codes multilevel coding quasi-cyclic low-density parity-check codes rate-adaptivity zipper codes

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low-complexity Zipper-LDPC and low-Latency Zipper-BCH Concatenated codes

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JOURNAL OF LIGHTWAVE TECHNOLOGY 2023年第24期41卷 7328-7335页

作者： Barakatain, Masoud Hashemi, Yoones Karimi, Bashirreza Ebrahimzad, Hamid Li, Chuandong Huawei Technol Co Ltd Kanata ON K2K 3J1 Canada Marvell Technol Inc Santa Clara CA 95054 USA

A novel concatenated forward error correction (FEC) scheme is proposed that consists of an inner zipper framework with low-density parity-check component codes and an outer zipper framework with BCH component codes. The proposed soft-decision inner codes have a universal, flexible, and implementation-friendly structure with low decoding complexity. The inner code is error-reducing, tasked with reducing the error rate on bits passed to the outer hard decision code below its threshold. The proposed outer codes have ultra-low overhead and are designed to have small decoding memory and latency. Computer simulations show that the proposed zipper-BCH codes can reduce the decoding latency and required memory by up to a factor of 30, compared to the conventional zipper codes, while maintaining a minimal performance loss. The proposed scheme is considered with higher-order modulation with both multi-level coding and bit-interleaved coded modulation. Simulations show that the concatenated FEC scheme can provide a 0.1 dB gain over the state-of-the-art FEC designs, making it a highly attractive FEC solution for high-throughput optical communication systems.

关键词： Coded modulation concatenated coding fiber-optic communications forward error correction low-complexity codes low-density parity-check codes zipper codes

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Polar codes' Simplicity, Random codes' Durability

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IEEE TRANSACTIONS ON INFORMATION THEORY 2021年第3期67卷 1478-1508页

作者： Wang, Hsin-Po Duursma, Iwan M. Univ Illinois Dept Math Urbana IL 61801 USA

Over any discrete memoryless channel, we offer error correction codes such that: for one, their block error probabilities and code rates scale like random codes';and for two, their encoding and decoding complexities scale like polar codes'. Quantitatively, for any constants pi, rho > 0 such that pi +2 rho < 1 , we construct a sequence of block codes with block length N approaching infinity, block error probability exp (-N-pi) , code rate N-rho less than the Shannon capacity, and encoding and decoding complexity O(N\log N) per code block. The core theme is to incorporate polar coding (which limits the complexity to polar's realm) with large, random, dynamic kernels (which boosts the performance to random's realm). The putative codes are optimal in the following manner: Should pi +2 rho >1 , no such codes exist over generic channels regardless of complexity.

关键词： Kernel Polar codes Error probability Decoding complexity theory Memoryless systems Capacity planning Capacity-achieving codes low-complexity codes polar codes random codes

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Not Just for Errors: codes for Fast and Secure Flash Storage

Not Just for Errors: Codes for Fast and Secure Flash Storage

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Globecom Workshops

作者： Cassuto, Yuval Ecole Polytech Fed Lausanne Sch Comp & Commun Sci ALGO Lab CH-1015 Lausanne Switzerland

ISBN: (纸本)9781424488650

Error-correcting codes are normally employed in storage devices to guarantee the integrity of data in the presence of errors. This paper presents two schemes where error-correcting codes are used for entirely different purposes. In the first part of the paper, a new coding paradigm is proposed to improve the write performance of multi-level flash devices. By slightly relaxing the accuracy of cell programming, significant speed-up can be achieved. The resulting write inaccuracies are then corrected by codes that are tailored for the appropriately restricted error model. In the second part, new low-complexity codes are proposed to protect the security of sensitive data in the presence of imperfect physical erasure processes. codes that have optimal encoding and decoding complexities are constructed to allow fast storing and retrieval of secret data, and guarantee unconditional security of data against an adversary with access to parts of the secret that failed to erase.

关键词： cell programming decoding decoding complexity encoding complexity error correction codes error-correcting codes flash memories low-complexity codes multilevel flash storage devices security of data sensitive data security

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Log-Logarithmic Time Pruned Polar Coding

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IEEE TRANSACTIONS ON INFORMATION THEORY 2021年第3期67卷 1509-1521页

作者： Wang, Hsin-Po Duursma, Iwan M. Univ Illinois Dept Math Urbana IL 61801 USA

A pruned variant of polar coding is proposed for binary erasure channel (BEC). Fix any BEC. For sufficiently small epsilon > 0 , we construct a series of capacity achieving codes with block length N=epsilon(-4.9) , code rate R=Capacity-O(epsilon) , block error probability P = epsilon , and encoding and decoding time complexity bC = O(log vertical bar log epsilon vertical bar) per information bit. The given per-bit complexity bC is log-logarithmic in N, in Capacity-R , and in P. Beyond BEC, there is a generalization: Fix a prime q and fix a symmetric, q-ary-input, discrete-output memoryless channel. For sufficiently small epsilon > 0 , we construct a series of error correction codes with block length N=epsilon(-constant) , code rate R = Capacity - O(epsilon) , block error probability P = epsilon, and encoding and decoding time complexity bC =O(log vertical bar log epsilon vertical bar) per information bit. Over general channels, this family of codes has the lowest per-bit time complexity among all capacity-achieving codes known to date.

关键词： Polar codes Decoding Time complexity Parity check codes complexity theory Pins Error probability Capacity-achieving codes low-complexity codes polar codes tree pruning

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Rate-adaptive Concatenated Multilevel Coding with Fixed Decoding complexity 11

Rate-adaptive Concatenated Multilevel Coding with Fixed Deco...

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11th International Symposium on Topics in Coding (ISTC)

作者： Mehmood, Tayyab Yankov, Metodi P. Forchhammer, Soren Tech Univ Denmark Dept Photon Engn Lyngby Denmark

ISBN: (纸本)9781665409438

In this work, a low-complexity multilevel coding (MLC) based coded modulation approach having rate flexibility with two degrees of freedom is proposed. It consists of an inner soft-decision (SD) polar code serially concatenated with an outer hard-decision (HD) code. For a given HD outer code, a method is developed to optimize a multi-stage decoding based MLC scheme so that it will require a fixed amount of inner decoding operations and thereby having constant complexity while changing the transmission rate with near-continuous granularity. Over the range of studied transmission rates, the proposed MLC scheme with outer staircase code and zipper code utilizes 75%, and 73% fewer inner SD decodings, respectively, compared to BICM. Compared to the existing MLC approaches, the proposed MLC scheme, with same inner and outer codes, provides up to 72% reduction in the number of required inner SD decodings.

关键词： Rate flexibility low-complexity codes concatenated codes polar codes staircase codes zipper codes

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