1,638 research outputs found
Iterative Algebraic Soft-Decision List Decoding of Reed-Solomon Codes
In this paper, we present an iterative soft-decision decoding algorithm for
Reed-Solomon codes offering both complexity and performance advantages over
previously known decoding algorithms. Our algorithm is a list decoding
algorithm which combines two powerful soft decision decoding techniques which
were previously regarded in the literature as competitive, namely, the
Koetter-Vardy algebraic soft-decision decoding algorithm and belief-propagation
based on adaptive parity check matrices, recently proposed by Jiang and
Narayanan. Building on the Jiang-Narayanan algorithm, we present a
belief-propagation based algorithm with a significant reduction in
computational complexity. We introduce the concept of using a
belief-propagation based decoder to enhance the soft-input information prior to
decoding with an algebraic soft-decision decoder. Our algorithm can also be
viewed as an interpolation multiplicity assignment scheme for algebraic
soft-decision decoding of Reed-Solomon codes.Comment: Submitted to IEEE for publication in Jan 200
A comparison of VLSI architectures for time and transform domain decoding of Reed-Solomon codes
It is well known that the Euclidean algorithm or its equivalent, continued fractions, can be used to find the error locator polynomial needed to decode a Reed-Solomon (RS) code. It is shown that this algorithm can be used for both time and transform domain decoding by replacing its initial conditions with the Forney syndromes and the erasure locator polynomial. By this means both the errata locator polynomial and the errate evaluator polynomial can be obtained with the Euclidean algorithm. With these ideas, both time and transform domain Reed-Solomon decoders for correcting errors and erasures are simplified and compared. As a consequence, the architectures of Reed-Solomon decoders for correcting both errors and erasures can be made more modular, regular, simple, and naturally suitable for VLSI implementation
Architectures for soft-decision decoding of non-binary codes
En esta tesis se estudia el dise¿no de decodificadores no-binarios para la correcci'on
de errores en sistemas de comunicaci'on modernos de alta velocidad. El objetivo
es proponer soluciones de baja complejidad para los algoritmos de decodificaci'on
basados en los c'odigos de comprobaci'on de paridad de baja densidad no-binarios
(NB-LDPC) y en los c'odigos Reed-Solomon, con la finalidad de implementar arquitecturas
hardware eficientes.
En la primera parte de la tesis se analizan los cuellos de botella existentes en los
algoritmos y en las arquitecturas de decodificadores NB-LDPC y se proponen soluciones
de baja complejidad y de alta velocidad basadas en el volteo de s'¿mbolos.
En primer lugar, se estudian las soluciones basadas en actualizaci'on por inundaci
'on con el objetivo de obtener la mayor velocidad posible sin tener en cuenta la
ganancia de codificaci'on. Se proponen dos decodificadores diferentes basados en
clipping y t'ecnicas de bloqueo, sin embargo, la frecuencia m'axima est'a limitada
debido a un exceso de cableado. Por este motivo, se exploran algunos m'etodos
para reducir los problemas de rutado en c'odigos NB-LDPC. Como soluci'on se
propone una arquitectura basada en difusi'on parcial para algoritmos de volteo
de s'¿mbolos que mitiga la congesti'on por rutado. Como las soluciones de actualizaci
'on por inundaci'on de mayor velocidad son sub-'optimas desde el punto de
vista de capacidad de correci'on, decidimos dise¿nar soluciones para la actualizaci'on
serie, con el objetivo de alcanzar una mayor velocidad manteniendo la ganancia
de codificaci'on de los algoritmos originales de volteo de s'¿mbolo. Se presentan dos
algoritmos y arquitecturas de actualizaci'on serie, reduciendo el 'area y aumentando
de la velocidad m'axima alcanzable. Por 'ultimo, se generalizan los algoritmos de
volteo de s'¿mbolo y se muestra como algunos casos particulares puede lograr una
ganancia de codificaci'on cercana a los algoritmos Min-sum y Min-max con una
menor complejidad. Tambi'en se propone una arquitectura eficiente, que muestra
que el 'area se reduce a la mitad en comparaci'on con una soluci'on de mapeo directo.
En la segunda parte de la tesis, se comparan algoritmos de decodificaci'on Reed-
Solomon basados en decisi'on blanda, concluyendo que el algoritmo de baja complejidad
Chase (LCC) es la soluci'on m'as eficiente si la alta velocidad es el objetivo principal. Sin embargo, los esquemas LCC se basan en la interpolaci'on, que introduce
algunas limitaciones hardware debido a su complejidad. Con el fin de reducir
la complejidad sin modificar la capacidad de correcci'on, se propone un esquema
de decisi'on blanda para LCC basado en algoritmos de decisi'on dura. Por 'ultimo
se dise¿na una arquitectura eficiente para este nuevo esquemaGarcía Herrero, FM. (2013). Architectures for soft-decision decoding of non-binary codes [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/33753TESISPremiad
AONT-LT: a Data Protection Scheme for Cloud and Cooperative Storage Systems
We propose a variant of the well-known AONT-RS scheme for dispersed storage
systems. The novelty consists in replacing the Reed-Solomon code with rateless
Luby transform codes. The resulting system, named AONT-LT, is able to improve
the performance by dispersing the data over an arbitrarily large number of
storage nodes while ensuring limited complexity. The proposed solution is
particularly suitable in the case of cooperative storage systems. It is shown
that while the AONT-RS scheme requires the adoption of fragmentation for
achieving widespread distribution, thus penalizing the performance, the new
AONT-LT scheme can exploit variable length codes which allow to achieve very
good performance and scalability.Comment: 6 pages, 8 figures, to be presented at the 2014 High Performance
Computing & Simulation Conference (HPCS 2014) - Workshop on Security, Privacy
and Performance in Cloud Computin
Media-Based MIMO: A New Frontier in Wireless Communications
The idea of Media-based Modulation (MBM), is based on embedding information
in the variations of the transmission media (channel state). This is in
contrast to legacy wireless systems where data is embedded in a Radio Frequency
(RF) source prior to the transmit antenna. MBM offers several advantages vs.
legacy systems, including "additivity of information over multiple receive
antennas", and "inherent diversity over a static fading channel". MBM is
particularly suitable for transmitting high data rates using a single transmit
and multiple receive antennas (Single Input-Multiple Output Media-Based
Modulation, or SIMO-MBM). However, complexity issues limit the amount of data
that can be embedded in the channel state using a single transmit unit. To
address this shortcoming, the current article introduces the idea of Layered
Multiple Input-Multiple Output Media-Based Modulation (LMIMO-MBM). Relying on a
layered structure, LMIMO-MBM can significantly reduce both hardware and
algorithmic complexities, as well as the training overhead, vs. SIMO-MBM.
Simulation results show excellent performance in terms of Symbol Error Rate
(SER) vs. Signal-to-Noise Ratio (SNR). For example, a LMIMO-MBM is
capable of transmitting bits of information per (complex) channel-use,
with SER at dB (or SER
at dB). This performance is achieved using a single transmission
and without adding any redundancy for Forward-Error-Correction (FEC). This
means, in addition to its excellent SER vs. energy/rate performance, MBM
relaxes the need for complex FEC structures, and thereby minimizes the
transmission delay. Overall, LMIMO-MBM provides a promising alternative to MIMO
and Massive MIMO for the realization of 5G wireless networks.Comment: 26 pages, 11 figures, additional examples are given to further
explain the idea of Media-Based Modulation. Capacity figure adde
Architecture for time or transform domain decoding of reed-solomon codes
Two pipeline (255,233) RS decoders, one a time domain decoder and the other a transform domain decoder, use the same first part to develop an errata locator polynomial .tau.(x), and an errata evaluator polynominal A(x). Both the time domain decoder and transform domain decoder have a modified GCD that uses an input multiplexer and an output demultiplexer to reduce the number of GCD cells required. The time domain decoder uses a Chien search and polynomial evaluator on the GCD outputs .tau.(x) and A(x), for the final decoding steps, while the transform domain decoder uses a transform error pattern algorithm operating on .tau.(x) and the initial syndrome computation S(x), followed by an inverse transform algorithm in sequence for the final decoding steps prior to adding the received RS coded message to produce a decoded output message
EVENODD: An Efficient Scheme for Tolerating Double Disk Failures in RAID Architectures
We present a novel method, that we call EVENODD, for tolerating up to two disk failures in RAID architectures. EVENODD employs the addition of only two redundant disks and consists of simple exclusive-OR computations. This redundant storage is optimal, in the sense that two failed disks cannot be retrieved with less than two redundant disks. A major advantage of EVENODD is that it only requires parity hardware, which is typically present in standard RAID-5 controllers. Hence, EVENODD can be implemented on standard RAID-5 controllers without any hardware changes. The most commonly used scheme that employes optimal redundant storage (i.e., two extra disks) is based on Reed-Solomon (RS) error-correcting codes. This scheme requires computation over finite fields and results in a more complex implementation. For example, we show that the complexity of implementing EVENODD in a disk array with 15 disks is about 50% of the one required when using the RS scheme. The new scheme is not limited to RAID architectures: it can be used in any system requiring large symbols and relatively short codes, for instance, in multitrack magnetic recording. To this end, we also present a decoding algorithm for one column (track) in error
A Simplified Min-Sum Decoding Algorithm for Non-Binary LDPC Codes
Non-binary low-density parity-check codes are robust to various channel
impairments. However, based on the existing decoding algorithms, the decoder
implementations are expensive because of their excessive computational
complexity and memory usage. Based on the combinatorial optimization, we
present an approximation method for the check node processing. The simulation
results demonstrate that our scheme has small performance loss over the
additive white Gaussian noise channel and independent Rayleigh fading channel.
Furthermore, the proposed reduced-complexity realization provides significant
savings on hardware, so it yields a good performance-complexity tradeoff and
can be efficiently implemented.Comment: Partially presented in ICNC 2012, International Conference on
Computing, Networking and Communications. Accepted by IEEE Transactions on
Communication
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