Noah Bray-Ali, David Chester, Dugan Hammock et al. · arXiv (Cornell University) · 2019
Holographic codes grown with perfect tensors on regular hyperbolic tessellations using an inflation rule protect quantum information stored in the bulk from errors on the boundary provided the code rate is less than one. Hyperbolic geometry bounds the holographic code rate and guarantees quantum error correction for codes grown with any inflation rule on all regular hyperbolic tessellations in a class whose size grows exponentially with the rank of the perfect tensors for rank five and higher. For the tile completion inflation rule, holographic triangle codes have code rate more than one but all others perform quantum error correction.
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Pfaff, Amrei · Figshare · 2021
code used or calculating relative grooming rates
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Multiplexing Ochm In, Jae Kyun Kwon A, Suwon Park B et al. · 2003
We previously proposed an Orthogonal Code Hopping Multiplexing(OCHM) scheme as a new statistical multiplexing scheme in synchronous downlink. OCHM enables a large number of users to share a limited number of code channels through statistical multiplexing. In this paper, we obtain the optimal code rate in several traffic load environments by simulation and summarize the appropriate traffic load region for each code rate as the optimal code rate. An adaptive code rate control scheme is proposed and the base station adaptively changes the code rate according to traffic environments in order to save power.
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Mingming · Zenodo (CERN European Organization for Nuclear Research) · 2026
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Adams, Dean C., Collyer, Michael · DRYAD · 2016
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Mingming · Zenodo (CERN European Organization for Nuclear Research) · 2026
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John Lodge · 2007
INTRODUCTION This paper presents design techniques and performance for forward error correction (FEC) codes formed using single-parity-bit component codes. Iteratively-decodable (e.g., "turbo" decodable) codes constructed using only single-parity-bit component codes have been investigated by a number of researchers in the past; for example [1,2,3,4]. This class of codes is particularly well suited to high coderate applications, as compared to turbo-codes [5], which excel at low to moderate code rates. Furthermore, the highly parallel nature and the simple component code decoders allow very high-speed implementation. For example, using the Galaxy product of Advanced Hardware Architectures Inc., HyperCodes [3] can be implemented at data rates in excess of the OC-3 rate of 155 Mbps. However, similar to turbo-codes, this class of codes can experience a "flattening" or "flaring" of the bit-error rate curve at high signal-to-noise ratios (SNR) that limits the ultimate power efficiency
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Rajesh Neelakandan, K. Ganesan · IEEE Access · 2024
Index coding is an elegant and powerful idea for minimal usage of broadcast channels that investigates the fundamental limits and optimal coding schemes in information flow networks such as wireless networks, data storage networks, and content delivery networks. Minimal usage of broadcast channels is the main requirement of efficient information broadcasting in information flow networks which is the ultimate goal for successful communication. Finding the optimal index code with extreme rate for the class of index coding problems is the fundamental question in index coding. In this work, we present a new class of index coding problems with the size of maximum acyclic induced subgraph = 3. We refer to this class of index coding problems as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$class \mathbb {III}$ </tex-math></inline-formula> index coding problems. Our goal is to characterize the extreme rate (i.e., the optimal index code length for extreme rate) for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$class \mathbb {III}$ </tex-math></inline-formula> index coding problems. We show that the optimal linear index code of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$class \mathbb {III}$ </tex-math></inline-formula> index coding problem over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbb {F}_{2}$ </tex-math></inline-formula> achieves the extreme rate on the broadcast rate. To present this new result, we use the results of index coding network coding duality. In contrast with this new result, we also present that there exists maximum acyclic induced subgraph size 3 index coding problems with the optimal broadcast rate strictly greater than the extreme rate. To present this contrast, we use the alignment graph and the conflict hyper graph based approach.
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Erik Stauffer, D. Tujkovic, A. Paulraj · IEEE Transactions on Information Theory · 2009
Multiple antenna systems can be used to increase system reliability or to increase system capacity. Initially, space-time codes were designed to achieve one of these two types of gain. Recently, though, a tradeoff between these two system resources has been characterized by the diversity-multiplexing tradeoff. Achieving this optimal performance frontier requires proper coding. For diversity optimality, the signal transmitted from each antenna must redundantly describe the message bits. This redundancy has been quantified by the rate of a space-time code, which relates space-time codebook size to constituent single-input-single-output (SISO) constellation size. Achievable diversity has also been shown to decrease with increasing rates, which establishes the diversity-rate tradeoff. In this work, we consider a generalized notion of the rate of the space-time code, which we refer to as the code rate Rc, and the associated diversity-code rate tradeoff. We then generalize the diversity-multiplexing and diversity-code rate tradeoffs and find that a new diversity-multiplexing tradeoff exists as a function of the code rate.
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Agnieszka Pręgowska, Janusz Szczepański, Eligiusz Wajnryb · Neurocomputing · 2016
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Tadashi Wadayama Koichiro, Koichiro Wakasugi, Masao Kasahara · 2007
this paper, for inner code, we construct the high rate BC codes by maximizing the effective minimum distance. With the new inner codes, we can decrease the decoding complexity of the inner code compared with conventional best convolutional code while maintaining the overall decoding performance.
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Jae Kyun Kwon, See Profile, Suwon Park et al. · 2003
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Jean‐Marc Edeline · 2005
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William C. Lemon, Wayne M. Getz · Biosystems · 2000
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Minseo Kim, Jongsun Park · 2022 19th International SoC Design Conference (ISOCC) · 2022
With the aggressive scaling of DRAM process technology, the reliability degradation has become a critical issue, which inevitably increases the demand for more powerful error correction code (ECC) than conventional Hamming code. Although double error correction (DEC) BCH code needs less parity bits than other DEC codes, it cannot detect the errors larger than 3 bits. In this paper, we present a novel BCH code combined with cyclic redundancy check (CRC) code which can effectively detect multi-bit errors. By employing the CRC code, the proposed BCH code corrects double errors with a 3-bit error detection probability of 84%. In addition, by reusing the BCH encoder as CRC encoder and decoder in the proposed BCH, the area overhead of the proposed BCH is only 7.8<sup>%</sup> compared to the conventional BCH code.
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Jian Li, Tongtong Li, Jian Ren · 2015
Regenerating code is a class of code very suitable for distributed storage systems, which can maintain optimal bandwidth and storage space. Two types of important regenerating code have been constructed: the minimum storage regeneration (MSR) code and the minimum bandwidth regeneration (MBR) code. However, in hostile networks where adversaries can compromise storage nodes, the storage capacity of the network can be significantly affected. In this paper, we propose a rate-matched MSR code that can combat against this kind of adversaries in hostile networks. We optimize the code parameters for given system requirements. Our comprehensive analysis shows that our code can detect and correct malicious nodes with higher storage efficiency compared to the normal error correction MSR code.
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Ma, Yanhong, Lan, Tian · Figshare · 2022
The Matlab code used in numerical calculation that solving the rate equations.
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Juzi Zhao, Yan Li, Henk Wymeersch et al. · Chalmers Research (Chalmers University of Technology) · 2015
We combine adaptive coding with nonlinear impairment-aware routing and spectrum allocation problem in elastic optical networks. An integer linear program formulation and low-complexity heuristics are proposed. Results indicate that over 50% bandwidth reduction can be obtained due to code-rate optimization.
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R. Kwan, Josep Colom Ikuno · Electronics Letters · 2013
Proposed is an intuitive model for the effective code rate of HARQ‐coded LTE transmissions. The model is derived from the circular structure of the rate matching buffer employed in LTE. Comparison with prior results, which were obtained by empirically extracting the code rates from the rate matcher, show the accuracy of the presented, entirely analytical, model.
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Theodore Sokoloski A, Johannes Opfermann B, Jeffrey Brum A et al. · 2015
Micronization of powders can lead to high-energy sites that probably are confined to the surface. Spray drying or freeze drying of the same material can lead to a bulk or contiguous high-energy material. We attempt to answer the following questions: Is the energy of the presumed amorphous state the same in both? Do we know with certainty the extent of amorphous content in either? Characterizing the rate and extent of water mediated conversion in the two high-energy materials via isothermal calorimetry and gravimetry has the potential for making this measurement and discrimination. Amorphous lactose (via XPRD) is exposed to 50 % RH in an isothermal microcalorimeter (TAM) and an isothermal microbalance (DVS). Heat flow or mass is measured as a function of time in a sorption region (before any crystallization) at 5 temperatures with n = 8 or 9. Friedman analysis shows the reaction to be more than one step. Formal kinetic analysis via NETZSCH Thermokinetics ® suggested several potential mechanisms. XPRD is used to detect crystallinity in the product. Solid-state NMR is used to detect the presence of a and b forms present in reactant and product [1]. A plausible mechanism might be a three step consecutive process: A&gt;B, 1st order (adsorption); B&gt;C, rate limiting 1-dimentional diffusion (spray dried product consists of hollow microspheres with shell
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