Error-Erasure Decoding of Linearized Reed-Solomon Codes in the Sum-Rank Metric

Hörmann, Felicitas; Bartz, Hannes; Puchinger, Sven

doi:10.48550/arxiv.2202.06758

Cited by 2 publications

(4 citation statements)

References 19 publications

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“…VII-D], a sum-rank BCH code (used in Proposition 34) may be decoded for the sum-rank metric by decoding the corresponding linearized Reed-Solomon code. Since these latter codes may correct sum-rank errors and erasures (by rows and columns) by [8], then the same holds for the codes in Proposition 34, by Corollary 30 and Proposition 31.…”

Section: Some Explicit Codesmentioning

confidence: 73%

“…We consider both column and row erasures, which was first considered in [21]. Item 2 is included since it was the formulation used in [8,21], but the connection with the multi-cover metric is easier using Item 3. The equivalence between the two is proven as in [16,Prop.…”

Section: Codes In the Sum-rank Metricmentioning

confidence: 99%

“…Second, C can correct t errors and ρ erasures (in rows or columns) for the sum-rank metric, as in Item 2 in Proposition 29, with a complexity of O(s 2 t 2 ) sums and products over the finite field F q s , by the algorithm in [8]. By Corollary 30 and Proposition 31, we may decode ϕ(C) by using such a decoder u times.…”

Section: Some Explicit Codesmentioning

confidence: 99%

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Multilayer crisscross error and erasure correction

Martínez-Peñas¹

2022

Preprint

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In this work, multilayer crisscross error and erasures are considered, which affect entire rows and columns in the matrices of a list of matrices. To measure such errors and erasures, the multi-cover metric is introduced. Several bounds are derived, including a Singleton bound, and maximum multi-cover distance (MMCD) codes are defined as those attaining it. Duality, puncturing and shortening of linear MMCD codes are studied. It is shown that the dual of a linear MMCD code is not necessarily MMCD, and those satisfying this duality condition are defined as dually MMCD codes. Finally, some constructions of codes in the multi-cover metric are given, including dually MMCD codes, together with efficient decoding algorithms for them.

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Section: Some Explicit Codesmentioning

confidence: 73%

Section: Codes In the Sum-rank Metricmentioning

confidence: 99%

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Multilayer crisscross error and erasure correction

Martínez-Peñas¹

2022

Preprint

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“…The chance of each of these three options depends on the precise RS code that was selected, the number of errors, and the distribution of the errors. To summarize, a standard RS codeword typically contains k symbols for the source data and n-k symbols for redundancy (parity check) [8]. RS encoders can be constructed by LFSRs, while RS decoders are more difficult to design.…”

Section: Reed Solomon Theorymentioning

confidence: 99%

A VHDL Code for Offset Pulse Position Modulation Working with Reed Solomon System by Using ModelSim

Albatoosh

Shujaa

Al-Nedawe

2022

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Error correction codes, often known as ECC, play a significant part in the process of detecting and correcting data mistakes that occur through communication channels that are unreliable or noisy. The essential concept behind error correction through ECC is to supplement the message that is being sent by the transmitter with redundant bits, the values of which are determined by the parameters n and k. These bits can then be utilized by the receiver to identify and correct specific types of errors. ECC is utilized in a wide variety of applications, including but not limited to data storage, the Internet, and telecommunications. There are numerous variations of ECC, including linear block, convolutional, and turbo codes, among others. The results of a simulation of a linear block reed Solomon, for example, with offset pulse position modulation have been presented in this study. The simulation was carried out in very high-speed integrated circuit hardware description language (VHDL), and a field-programmable gate array was used (FPGA) It made use of a Boolean function to function to program code for an algorithm that is working. Because of its performance, time to market, cost, reliability, and long-term maintenance benefits, FPGA is an appropriate platform for implementing error correction code (ECC). As a part of this project, the technique of offset Pulse Position Modulation (Offset PPM) was invented as an outstanding solution to code the fiber-optic applications and Reed Solomon (RS) codes apply to ModelSim SE-64 10.5 software. In addition, this coding scheme has been approved by the simulation and is matched with theory, and it is expected to be implemented shortly. The study begins with a concise introduction to RS encode/decode about design and performance and then moves on to discuss the development result of simulation and hardware implementation.

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Error-Erasure Decoding of Linearized Reed-Solomon Codes in the Sum-Rank Metric

Cited by 2 publications

References 19 publications

Multilayer crisscross error and erasure correction

Multilayer crisscross error and erasure correction

A VHDL Code for Offset Pulse Position Modulation Working with Reed Solomon System by Using ModelSim

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