563 research outputs found
Soft-Decision Low-Complexity Chase Decoders for the RS(255,239) Code
[EN] In this work, we present a new architecture for soft-decision Reed-Solomon (RS) Low-Complexity Chase (LCC) decoding. The proposed architecture is scalable and can be used for a high number of test vectors. We propose a novel Multiplicity Assignment stage that sorts and stores only the location of the errors inside the symbols and the powers of a that identify the positions of the symbols in the frame. Novel schematics for the Syndrome Update and Symbol Modification blocks that are adapted to the proposed sorting stage are also presented. We also propose novel solutions for the problems that arise when a high number of test vectors is processed. We implemented three decoders: a h = 4 LCC decoder and two decoders that only decode 31 and 60 test vectors of true h = 5 and h = 6 LCC decoders, respectively. For example, our h = 4 decoder requires 29% less look-up tables in Virtex-V Field Programmable Gate Array (FPGA) devices than the best soft-decision RS decoder published to date, while has a 0.07 dB coding gain over that decoder.This research was funded by the Spanish Ministerio de Economia y Competitividad and FEDER grant number TEC2015-70858-C2-2-RTorres Carot, V.; Valls Coquillat, J.; Canet Subiela, MJ.; GarcĂa Herrero, FM. (2019). Soft-Decision Low-Complexity Chase Decoders for the RS(255,239) Code. Electronics. 8(1):1-13. https://doi.org/10.3390/electronics8010010S11381Cideciyan, R., Gustlin, M., Li, M., Wang, J., & Wang, Z. (2013). Next generation backplane and copper cable challenges. IEEE Communications Magazine, 51(12), 130-136. doi:10.1109/mcom.2013.6685768Koetter, R., & Vardy, A. (2003). Algebraic soft-decision decoding of reed-solomon codes. IEEE Transactions on Information Theory, 49(11), 2809-2825. doi:10.1109/tit.2003.819332Sudan, M. (1997). Decoding of Reed Solomon Codes beyond the Error-Correction Bound. Journal of Complexity, 13(1), 180-193. doi:10.1006/jcom.1997.0439Guruswami, V., & Sudan, M. (1999). Improved decoding of Reed-Solomon and algebraic-geometry codes. IEEE Transactions on Information Theory, 45(6), 1757-1767. doi:10.1109/18.782097Jiang, J., & Narayanan, K. R. (2008). Algebraic Soft-Decision Decoding of Reed–Solomon Codes Using Bit-Level Soft Information. IEEE Transactions on Information Theory, 54(9), 3907-3928. doi:10.1109/tit.2008.928238Jiangli Zhu, Xinmiao Zhang, & Zhongfeng Wang. (2009). Backward Interpolation Architecture for Algebraic Soft-Decision Reed–Solomon Decoding. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 17(11), 1602-1615. doi:10.1109/tvlsi.2008.2005575Jiangli Zhu, & Xinmiao Zhang. (2008). Efficient VLSI Architecture for Soft-Decision Decoding of Reed–Solomon Codes. IEEE Transactions on Circuits and Systems I: Regular Papers, 55(10), 3050-3062. doi:10.1109/tcsi.2008.923169Zhongfeng Wang, & Jun Ma. (2006). High-Speed Interpolation Architecture for Soft-Decision Decoding of Reed–Solomon Codes. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 14(9), 937-950. doi:10.1109/tvlsi.2006.884046Zhang, X. (2006). Reduced Complexity Interpolation Architecture for Soft-Decision Reed–Solomon Decoding. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 14(10), 1156-1161. doi:10.1109/tvlsi.2006.884177Xinmiao Zhang, & Parhi, K. K. (2005). Fast factorization architecture in soft-decision Reed-Solomon decoding. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 13(4), 413-426. doi:10.1109/tvlsi.2004.842914Bellorado, J., & Kavcic, A. (2010). Low-Complexity Soft-Decoding Algorithms for Reed–Solomon Codes—Part I: An Algebraic Soft-In Hard-Out Chase Decoder. IEEE Transactions on Information Theory, 56(3), 945-959. doi:10.1109/tit.2009.2039073GarcĂa-Herrero, F., Valls, J., & Meher, P. K. (2011). High-Speed RS(255, 239) Decoder Based on LCC Decoding. Circuits, Systems, and Signal Processing, 30(6), 1643-1669. doi:10.1007/s00034-011-9327-4Zhang, W., Wang, H., & Pan, B. (2013). Reduced-Complexity LCC Reed–Solomon Decoder Based on Unified Syndrome Computation. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 21(5), 974-978. doi:10.1109/tvlsi.2012.2197030Peng, X., Zhang, W., Ji, W., Liang, Z., & Liu, Y. (2015). Reduced-Complexity Multiplicity Assignment Algorithm and Architecture for Low-Complexity Chase Decoder of Reed-Solomon Codes. IEEE Communications Letters, 19(11), 1865-1868. doi:10.1109/lcomm.2015.2477495Lin, Y.-M., Hsu, C.-H., Chang, H.-C., & Lee, C.-Y. (2014). A 2.56 Gb/s Soft RS (255, 239) Decoder Chip for Optical Communication Systems. IEEE Transactions on Circuits and Systems I: Regular Papers, 61(7), 2110-2118. doi:10.1109/tcsi.2014.2298282Wu, Y. (2015). New Scalable Decoder Architectures for Reed–Solomon Codes. IEEE Transactions on Communications, 63(8), 2741-2761. doi:10.1109/tcomm.2015.2445759Garcia-Herrero, F., Canet, M. J., Valls, J., & Meher, P. K. (2012). High-Throughput Interpolator Architecture for Low-Complexity Chase Decoding of RS Codes. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 20(3), 568-573. doi:10.1109/tvlsi.2010.210396
A New Chase-type Soft-decision Decoding Algorithm for Reed-Solomon Codes
This paper addresses three relevant issues arising in designing Chase-type
algorithms for Reed-Solomon codes: 1) how to choose the set of testing
patterns; 2) given the set of testing patterns, what is the optimal testing
order in the sense that the most-likely codeword is expected to appear earlier;
and 3) how to identify the most-likely codeword. A new Chase-type soft-decision
decoding algorithm is proposed, referred to as tree-based Chase-type algorithm.
The proposed algorithm takes the set of all vectors as the set of testing
patterns, and hence definitely delivers the most-likely codeword provided that
the computational resources are allowed. All the testing patterns are arranged
in an ordered rooted tree according to the likelihood bounds of the possibly
generated codewords. While performing the algorithm, the ordered rooted tree is
constructed progressively by adding at most two leafs at each trial. The
ordered tree naturally induces a sufficient condition for the most-likely
codeword. That is, whenever the proposed algorithm exits before a preset
maximum number of trials is reached, the output codeword must be the
most-likely one. When the proposed algorithm is combined with Guruswami-Sudan
(GS) algorithm, each trial can be implement in an extremely simple way by
removing one old point and interpolating one new point. Simulation results show
that the proposed algorithm performs better than the recently proposed
Chase-type algorithm by Bellorado et al with less trials given that the maximum
number of trials is the same. Also proposed are simulation-based performance
bounds on the MLD algorithm, which are utilized to illustrate the
near-optimality of the proposed algorithm in the high SNR region. In addition,
the proposed algorithm admits decoding with a likelihood threshold, that
searches the most-likely codeword within an Euclidean sphere rather than a
Hamming sphere
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
Prefactor Reduction of the Guruswami-Sudan Interpolation Step
The concept of prefactors is considered in order to decrease the complexity
of the Guruswami-Sudan interpolation step for generalized Reed-Solomon codes.
It is shown that the well-known re-encoding projection due to Koetter et al.
leads to one type of such prefactors. The new type of Sierpinski prefactors is
introduced. The latter are based on the fact that many binomial coefficients in
the Hasse derivative associated with the Guruswami-Sudan interpolation step are
zero modulo the base field characteristic. It is shown that both types of
prefactors can be combined and how arbitrary prefactors can be used to derive a
reduced Guruswami-Sudan interpolation step.Comment: 13 pages, 3 figure
Architectures for soft-decision decoding of non-binary codes
En esta tesis se estudia el diseÂżno 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'Âżmbolos.
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'Âżmbolos 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 diseÂżnar 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'Âżmbolo. 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'Âżmbolo 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 diseÂżna una arquitectura eficiente para este nuevo esquemaGarcĂa 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
On the implementation of modified fuzzy vault for biometric encryption
Abstract—Biometrics, such as irises and fingerprints, enable se-cure and non-repudiable authentication. Fuzzy vault is a scheme that can monolithically bind secret to biometric templates. Moreover, the modified fuzzy vault (MFV) leads to less entropy loss and requires less memory for storing the sketches. This paper proposes a novel low-complexity scheme to compute the monic polynomial for the sketch during the enrollment process of the MFV. An innovative interpolation method is also developed to reduce the computation complexity and latency of the verification process. Efficient hardware implementation architectures are developed in this paper for the proposed schemes and their complexities are analyzed in detail. I
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