278 research outputs found
Improved Decoding of Staircase Codes: The Soft-aided Bit-marking (SABM) Algorithm
Staircase codes (SCCs) are typically decoded using iterative bounded-distance
decoding (BDD) and hard decisions. In this paper, a novel decoding algorithm is
proposed, which partially uses soft information from the channel. The proposed
algorithm is based on marking certain number of highly reliable and highly
unreliable bits. These marked bits are used to improve the
miscorrection-detection capability of the SCC decoder and the error-correcting
capability of BDD. For SCCs with -error-correcting
Bose-Chaudhuri-Hocquenghem component codes, our algorithm improves upon
standard SCC decoding by up to ~dB at a bit-error rate (BER) of
. The proposed algorithm is shown to achieve almost half of the gain
achievable by an idealized decoder with this structure. A complexity analysis
based on the number of additional calls to the component BDD decoder shows that
the relative complexity increase is only around at a BER of .
This additional complexity is shown to decrease as the channel quality
improves. Our algorithm is also extended (with minor modifications) to product
codes. The simulation results show that in this case, the algorithm offers
gains of up to ~dB at a BER of .Comment: 10 pages, 12 figure
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
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
Reliability Level List Based Iterative SISO Decoding Algorithm for Block Turbo Codes
An iterative Reliability Level List (RLL) based soft-input soft-output (SISO) decoding algorithm has been proposed for Block Turbo Codes (BTCs). The algorithm ingeniously adapts the RLL based decoding algorithm for the constituent block codes, which is a soft-input hard-output algorithm. The extrinsic information is calculated using the reliability of these hard-output decisions and is passed as soft-input to the iterative turbo decoding process. RLL based decoding of constituent codes estimate the optimal transmitted codeword through a directed minimal search. The proposed RLL based decoder for the constituent code replaces the Chase-2 based constituent decoder in the conventional SISO scheme. Simulation results show that the proposed algorithm has a clear advantage of performance improvement over conventional Chase-2 based SISO decoding scheme with reduced decoding latency at lower noise levels
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 esquemaGarcÃa 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
Compressed Shaping: Concept and FPGA Demonstration
Probabilistic shaping (PS) has been widely studied and applied to optical
fiber communications. The encoder of PS expends the number of bit slots and
controls the probability distribution of channel input symbols. Not only
studies focused on PS but also most works on optical fiber communications have
assumed source uniformity (i.e. equal probability of marks and spaces) so far.
On the other hand, the source information is in general nonuniform, unless
bit-scrambling or other source coding techniques to balance the bit probability
is performed. Interestingly, one can exploit the source nonuniformity to reduce
the entropy of the channel input symbols with the PS encoder, which leads to
smaller required signal-to-noise ratio at a given input logic rate. This
benefit is equivalent to a combination of data compression and PS, and thus we
call this technique compressed shaping. In this work, we explain its
theoretical background in detail, and verify the concept by both numerical
simulation and a field programmable gate array (FPGA) implementation of such a
system. In particular, we find that compressed shaping can reduce power
consumption in forward error correction decoding by up to 90% in nonuniform
source cases. The additional hardware resources required for compressed shaping
are not significant compared with forward error correction coding, and an error
insertion test is successfully demonstrated with the FPGA.Comment: 10 pages, 12 figure
Successive Cancellation Ordered Search Decoding of Modified -Coset Codes
A tree search algorithm called successive cancellation ordered search (SCOS)
is proposed for -coset codes that implements
maximum-likelihood (ML) decoding with an adaptive complexity for transmission
over binary-input AWGN channels. Unlike bit-flip decoders, no outer code is
needed to terminate decoding; therefore, SCOS also applies to
-coset codes modified with dynamic frozen bits. The average
complexity is close to that of successive cancellation (SC) decoding at
practical frame error rates (FERs) for codes with wide ranges of rate and
lengths up to bits, which perform within dB or less from the
random coding union bound and outperform Reed--Muller codes under ML decoding
by up to dB. Simulations illustrate simultaneous gains for SCOS over
SC-Fano, SC stack (SCS) and SC list (SCL) decoding in FER and the average
complexity at various SNR regimes. SCOS is further extended by forcing it to
look for candidates satisfying a threshold on the likelihood, thereby
outperforming basic SCOS under complexity constraints. The modified SCOS
enables strong error-detection capability without the need for an outer code.
In particular, the PAC code under modified SCOS provides gains in
overall and undetected FER compared to CRC-aided polar codes under SCL/dynamic
SC flip decoding at high SNR.Comment: 14 pages, 9 figures, 3 tables. Submitted to IEEE journal. The revised
version of the first submission. Major changes: 1) No dedicated section for
numerical results. Instead, simulations are provided right after the relevant
section. 2) More simulation results are added to compare all the state of art
polar decoders in terms of the number of arithmetic operations. arXiv admin
note: text overlap with arXiv:2105.0404
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