6,007 research outputs found
Fourier transform over finite groups for error detection and error correction in computation channels
We consider the methods of error detection and correction in devices and programs calculating functions f: G → K where G is a finite group and K is a field. For error detection and correction we use linear checks generated by convolutions in the field K of the original function f and some checking idempotent function δ: G → , 1 For the construction of the optimal checking function δ we use methods of harmonic analysis over the group G in the field K. Since these methods will be the main tools for the construction of optimal checks, we consider the algorithms for the fast computation of Fourier Transforms over the group G in the field K. We solve the problem of error detecting and correcting capability for our methods for two important classes of decoding procedures (memoryless and memory-aided decoding) and consider the question of syndrome computation for these methods. We describe also properties of error correcting codes generated by convolution checks
Quantum computing and the entanglement frontier - Rapporteur talk at the 25th Solvay Conference
Quantum information science explores the frontier of highly complex quantum states,
the "entanglement frontier". This study is motivated by the observation (widely believed
but unproven) that classical systems cannot simulate highly entangled quantum systems
efficiently, and we hope to hasten the day when well controlled quantum systems can
perform tasks surpassing what can be done in the classical world. One way to achieve
such "quantum supremacy" would be to run an algorithm on a quantum computer which
solves a problem with a super-polynomial speedup relative to classical computers, but
there may be other ways that can be achieved sooner, such as simulating exotic quantum
states of strongly correlated matter. To operate a large scale quantum computer reliably
we will need to overcome the debilitating effects of decoherence, which might be done
using "standard" quantum hardware protected by quantum error-correcting codes, or by
exploiting the nonabelian quantum statistics of anyons realized in solid state systems,
or by combining both methods. Only by challenging the entanglement frontier will we
learn whether Nature provides extravagant resources far beyond what the classical world
would allow
Techniques for the realization of ultrareliable spaceborne computers Interim scientific report
Error-free ultrareliable spaceborne computer
The Error-Pattern-Correcting Turbo Equalizer
The error-pattern correcting code (EPCC) is incorporated in the design of a
turbo equalizer (TE) with aim to correct dominant error events of the
inter-symbol interference (ISI) channel at the output of its matching Viterbi
detector. By targeting the low Hamming-weight interleaved errors of the outer
convolutional code, which are responsible for low Euclidean-weight errors in
the Viterbi trellis, the turbo equalizer with an error-pattern correcting code
(TE-EPCC) exhibits a much lower bit-error rate (BER) floor compared to the
conventional non-precoded TE, especially for high rate applications. A
maximum-likelihood upper bound is developed on the BER floor of the TE-EPCC for
a generalized two-tap ISI channel, in order to study TE-EPCC's signal-to-noise
ratio (SNR) gain for various channel conditions and design parameters. In
addition, the SNR gain of the TE-EPCC relative to an existing precoded TE is
compared to demonstrate the present TE's superiority for short interleaver
lengths and high coding rates.Comment: This work has been submitted to the special issue of the IEEE
Transactions on Information Theory titled: "Facets of Coding Theory: from
Algorithms to Networks". This work was supported in part by the NSF
Theoretical Foundation Grant 0728676
DNA Linear Block Codes: Generation, Error-detection and Error-correction of DNA Codeword
In modern age, the increasing complexity of computation and communication
technology is leading us towards the necessity of new paradigm. As a result,
unconventional approach like DNA coding theory is gaining considerable
attention. The storage capacity, information processing and transmission
properties of DNA molecules stimulate the notion of DNA coding theory as well
as DNA cryptography. In this paper we generate DNA codeword using DNA (n, k)
linear block codes which ensures the secure transmission of information. In the
proposed code design strategy DNA-based XOR operation (DNAX) is applied for
effective construction of DNA codewords which are quadruples generated over the
set of alphabets {A,T,G,C}. By worked out examples we explain the use of
generator matrix and parity check matrix in encryption and decryption of coded
data in the form of short single stranded DNA sequences. The newly developed
technique is capable of detecting as well as correcting error in transmission
of DNA codewords from sender to the intended receiver.Comment: 23 pages, 1 figure, 5 table
Error-correction coding for high-density magnetic recording channels.
Finally, a promising algorithm which combines RS decoding algorithm with LDPC decoding algorithm together is investigated, and a reduced-complexity modification has been proposed, which not only improves the decoding performance largely, but also guarantees a good performance in high signal-to-noise ratio (SNR), in which area an error floor is experienced by LDPC codes.The soft-decision RS decoding algorithms and their performance on magnetic recording channels have been researched, and the algorithm implementation and hardware architecture issues have been discussed. Several novel variations of KV algorithm such as soft Chase algorithm, re-encoded Chase algorithm and forward recursive algorithm have been proposed. And the performance of nested codes using RS and LDPC codes as component codes have been investigated for bursty noise magnetic recording channels.Future high density magnetic recoding channels (MRCs) are subject to more noise contamination and intersymbol interference, which make the error-correction codes (ECCs) become more important. Recent research of replacement of current Reed-Solomon (RS)-coded ECC systems with low-density parity-check (LDPC)-coded ECC systems obtains a lot of research attention due to the large decoding gain for LDPC-coded systems with random noise. In this dissertation, systems aim to maintain the RS-coded system using recent proposed soft-decision RS decoding techniques are investigated and the improved performance is presented
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