87,346 research outputs found
Functional diagnosability and recovery from massive faults in digital systems Quarterly progress reports, 17 May - 16 Nov. 1970 /final/
Diagnosability and recovery from massive faults in digital system
Nonuniform Fuchsian codes for noisy channels
We develop a new transmission scheme for additive white Gaussian noisy (AWGN)
channels based on Fuchsian groups from rational quaternion algebras. The
structure of the proposed Fuchsian codes is nonlinear and nonuniform, hence
conventional decoding methods based on linearity and symmetry do not apply.
Previously, only brute force decoding methods with complexity that is linear in
the code size exist for general nonuniform codes. However, the properly
discontinuous character of the action of the Fuchsian groups on the complex
upper half-plane translates into decoding complexity that is logarithmic in the
code size via a recently introduced point reduction algorithm
Graphical Structures for Design and Verification of Quantum Error Correction
We introduce a high-level graphical framework for designing and analysing
quantum error correcting codes, centred on what we term the coherent parity
check (CPC). The graphical formulation is based on the diagrammatic tools of
the zx-calculus of quantum observables. The resulting framework leads to a
construction for stabilizer codes that allows us to design and verify a broad
range of quantum codes based on classical ones, and that gives a means of
discovering large classes of codes using both analytical and numerical methods.
We focus in particular on the smaller codes that will be the first used by
near-term devices. We show how CSS codes form a subset of CPC codes and, more
generally, how to compute stabilizers for a CPC code. As an explicit example of
this framework, we give a method for turning almost any pair of classical
[n,k,3] codes into a [[2n - k + 2, k, 3]] CPC code. Further, we give a simple
technique for machine search which yields thousands of potential codes, and
demonstrate its operation for distance 3 and 5 codes. Finally, we use the
graphical tools to demonstrate how Clifford computation can be performed within
CPC codes. As our framework gives a new tool for constructing small- to
medium-sized codes with relatively high code rates, it provides a new source
for codes that could be suitable for emerging devices, while its zx-calculus
foundations enable natural integration of error correction with graphical
compiler toolchains. It also provides a powerful framework for reasoning about
all stabilizer quantum error correction codes of any size.Comment: Computer code associated with this paper may be found at
https://doi.org/10.15128/r1bn999672
AG codes and AG quantum codes from the GGS curve
In this paper, algebraic-geometric (AG) codes associated with the GGS maximal
curve are investigated. The Weierstrass semigroup at all -rational points of the curve is determined; the Feng-Rao designed
minimum distance is computed for infinite families of such codes, as well as
the automorphism group. As a result, some linear codes with better relative
parameters with respect to one-point Hermitian codes are discovered. Classes of
quantum and convolutional codes are provided relying on the constructed AG
codes
Fault Secure Encoder and Decoder for NanoMemory Applications
Memory cells have been protected from soft errors for more than a decade; due to the increase in soft error rate in logic circuits, the encoder and decoder circuitry around the memory blocks have become susceptible to soft errors as well and must also be protected. We introduce a new approach to design fault-secure encoder and decoder circuitry for memory designs. The key novel contribution of this paper is identifying and defining a new class of error-correcting codes whose redundancy makes the design of fault-secure detectors (FSD) particularly simple. We further quantify the importance of protecting encoder and decoder circuitry against transient errors, illustrating a scenario where the system failure rate (FIT) is dominated by the failure rate of the encoder and decoder. We prove that Euclidean geometry low-density parity-check (EG-LDPC) codes have the fault-secure detector capability. Using some of the smaller EG-LDPC codes, we can tolerate bit or nanowire defect rates of 10% and fault rates of 10^(-18) upsets/device/cycle, achieving a FIT rate at or below one for the entire memory system and a memory density of 10^(11) bit/cm^2 with nanowire pitch of 10 nm for memory blocks of 10 Mb or larger. Larger EG-LDPC codes can achieve even higher reliability and lower area overhead
Quantum error correction in crossbar architectures
A central challenge for the scaling of quantum computing systems is the need
to control all qubits in the system without a large overhead. A solution for
this problem in classical computing comes in the form of so called crossbar
architectures. Recently we made a proposal for a large scale quantum
processor~[Li et al. arXiv:1711.03807 (2017)] to be implemented in silicon
quantum dots. This system features a crossbar control architecture which limits
parallel single qubit control, but allows the scheme to overcome control
scaling issues that form a major hurdle to large scale quantum computing
systems. In this work, we develop a language that makes it possible to easily
map quantum circuits to crossbar systems, taking into account their
architecture and control limitations. Using this language we show how to map
well known quantum error correction codes such as the planar surface and color
codes in this limited control setting with only a small overhead in time. We
analyze the logical error behavior of this surface code mapping for estimated
experimental parameters of the crossbar system and conclude that logical error
suppression to a level useful for real quantum computation is feasible.Comment: 29 + 9 pages, 13 figures, 9 tables, 8 algorithms and 3 big boxes.
Comments are welcom
Sequential Circuit Design for Embedded Cryptographic Applications Resilient to Adversarial Faults
In the relatively young field of fault-tolerant cryptography, the main research effort has focused exclusively on the protection of the data path of cryptographic circuits. To date, however, we have not found any work that aims at protecting the control logic of these circuits against fault attacks, which thus remains the proverbial Achilles’ heel. Motivated by a hypothetical yet realistic fault analysis attack that, in principle, could be mounted against any modular exponentiation engine, even one with appropriate data path protection, we set out to close this remaining gap. In this paper, we present guidelines for the design of multifault-resilient sequential control logic based on standard Error-Detecting Codes (EDCs) with large minimum distance. We introduce a metric that measures the effectiveness of the error detection technique in terms of the effort the attacker has to make in relation to the area overhead spent in
implementing the EDC. Our comparison shows that the proposed EDC-based technique provides superior performance when compared against regular N-modular redundancy techniques. Furthermore, our technique scales well and does not affect the critical path delay
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