91 research outputs found
Low-Complexity Joint Channel Estimation and List Decoding of Short Codes
A pilot-assisted transmission (PAT) scheme is proposed for short
blocklengths, where the pilots are used only to derive an initial channel
estimate for the list construction step. The final decision of the message is
obtained by applying a non-coherent decoding metric to the codewords composing
the list. This allows one to use very few pilots, thus reducing the channel
estimation overhead. The method is applied to an ordered statistics decoder for
communication over a Rayleigh block-fading channel. Gains of up to dB as
compared to traditional PAT schemes are demonstrated for short codes with QPSK
signaling. The approach can be generalized to other list decoders, e.g., to
list decoding of polar codes.Comment: Accepted at the 12th International ITG Conference on Systems,
Communications and Coding (SCC 2019), Rostock, German
List Decoding of Short Codes for Communication over Unknown Fading Channels
In this paper, the advantages of list decoding for short packet transmission over fading channels with an unknown state are illustrated. The principle is applied to polar codes (under successive cancellation list decoding) and to general short binary linear block codes (under ordered-statistics decoding). The proposed decoders assume neither a-priori knowledge of the channel coefficients, nor of their statistics. The scheme relies on short pilot fields that are used only to derive an initial channel estimate. The channel estimate is required to be accurate enough to enable a good list construction, i.e., the construction of a list that contains, with high probability, the transmitted codeword. The final decision on the message is obtained by applying a list. This allows one to use very few pilots, thus reducing the the Rayleigh block-fading channel and compared to finite-length performance bounds. The proposed technique provides (in the short block length regime) gains of 1 dB with respect to a traditional pilot-aided transmission scheme
Design guidelines for spatial modulation
A new class of low-complexity, yet energyefficient Multiple-Input Multiple-Output (MIMO) transmission techniques, namely the family of Spatial Modulation (SM) aided MIMOs (SM-MIMO) has emerged. These systems are capable of exploiting the spatial dimensions (i.e. the antenna indices) as an additional dimension invoked for transmitting information, apart from the traditional Amplitude and Phase Modulation (APM). SM is capable of efficiently operating in diverse MIMO configurations in the context of future communication systems. It constitutes a promising transmission candidate for large-scale MIMO design and for the indoor optical wireless communication whilst relying on a single-Radio Frequency (RF) chain. Moreover, SM may also be viewed as an entirely new hybrid modulation scheme, which is still in its infancy. This paper aims for providing a general survey of the SM design framework as well as of its intrinsic limits. In particular, we focus our attention on the associated transceiver design, on spatial constellation optimization, on link adaptation techniques, on distributed/ cooperative protocol design issues, and on their meritorious variants
State-of-the-art space mission telecommand receivers
Since their dawning, space communications have been among the strongest driving applications for the development of error correcting codes. Indeed, space-to-Earth telemetry (TM) links have extensively exploited advanced coding schemes, from convolutional codes to Reed-Solomon codes (also in concatenated form) and, more recently, from turbo codes to low-density parity-check (LDPC) codes. The efficiency of these schemes has been extensively proved in several papers and reports. The situation is a bit different for Earth-to-space telecommand (TC) links. Space TCs must reliably convey control information as well as software patches from Earth control centers to scientific payload instruments and engineering equipment onboard (O/B) spacecraft. The success of a mission may be compromised because of an error corrupting a TC message: a detected error causing no execution or, even worse, an undetected error causing a wrong execution. This imposes strict constraints on the maximum acceptable detected and undetected error rates
Advanced channel coding techniques using bit-level soft information
In this dissertation, advanced channel decoding techniques based on bit-level soft information are studied. Two main approaches are proposed: bit-level probabilistic iterative decoding and bit-level algebraic soft-decision (list) decoding (ASD).
In the first part of the dissertation, we first study iterative decoding for high density parity check (HDPC) codes. An iterative decoding algorithm, which uses the sum product algorithm (SPA) in conjunction with a binary parity check matrix adapted in each decoding iteration according to the bit-level reliabilities is proposed. In contrast to the common belief that iterative decoding is not suitable for HDPC codes, this bit-level reliability based adaptation procedure is critical to the conver-gence behavior of iterative decoding for HDPC codes and it significantly improves the iterative decoding performance of Reed-Solomon (RS) codes, whose parity check matrices are in general not sparse. We also present another iterative decoding scheme for cyclic codes by randomly shifting the bit-level reliability values in each iteration. The random shift based adaptation can also prevent iterative decoding from getting stuck with a significant complexity reduction compared with the reliability based parity check matrix adaptation and still provides reasonable good performance for short-length cyclic codes.
In the second part of the dissertation, we investigate ASD for RS codes using bit-level soft information. In particular, we show that by carefully incorporating bit¬level soft information in the multiplicity assignment and the interpolation step, ASD can significantly outperform conventional hard decision decoding (HDD) for RS codes with a very small amount of complexity, even though the kernel of ASD is operating at the symbol-level. More importantly, the performance of the proposed bit-level ASD can be tightly upper bounded for practical high rate RS codes, which is in general not possible for other popular ASD schemes.
Bit-level soft-decision decoding (SDD) serves as an efficient way to exploit the potential gain of many classical codes, and also facilitates the corresponding per-formance analysis. The proposed bit-level SDD schemes are potential and feasible alternatives to conventional symbol-level HDD schemes in many communication sys-tems
CONVERGENCE IMPROVEMENT OF ITERATIVE DECODERS
Iterative decoding techniques shaked the waters of the error correction and communications
field in general. Their amazing compromise between complexity and performance
offered much more freedom in code design and made highly complex codes, that were
being considered undecodable until recently, part of almost any communication system.
Nevertheless, iterative decoding is a sub-optimum decoding method and as such, it has
attracted huge research interest. But the iterative decoder still hides many of its secrets,
as it has not been possible yet to fully describe its behaviour and its cost function.
This work presents the convergence problem of iterative decoding from various angles
and explores methods for reducing any sub-optimalities on its operation. The decoding
algorithms for both LDPC and turbo codes were investigated and aspects that contribute
to convergence problems were identified. A new algorithm was proposed, capable of providing
considerable coding gain in any iterative scheme. Moreover, it was shown that
for some codes the proposed algorithm is sufficient to eliminate any sub-optimality and
perform maximum likelihood decoding. Its performance and efficiency was compared to
that of other convergence improvement schemes.
Various conditions that can be considered critical to the outcome of the iterative decoder
were also investigated and the decoding algorithm of LDPC codes was followed
analytically to verify the experimental results
Coded cooperative diversity with low complexity encoding and decoding algorithms.
One of the main concerns in designing the wireless communication systems is to provide sufficiently large data rates while considering the different aspects of the implementation complexity that is often constrained by limited battery power and signal processing capability of the devices. Thus, in this thesis, a low complexity encoding and decoding algorithms are investigated for systems with the transmission diversity, particularly the receiver diversity and the cooperative diversity. Design guidelines for such systems are provided to provide a good trade-off between the implementation complexity and the performance. The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated to reduce the complexity of coded systems. The original order statistics decoding (OSD) is generalized by assuming segmentation of the most reliable independent positions of the received bits. The segmentation is shown to overcome several drawbacks of the original order statistics decoding. The complexity of the OSD is further reduced by assuming a partial ordering of the received bits in order to avoid the highly complex Gauss elimination. The bit error rate performance and the decoding complexity trade-off of the proposed decoding algorithms are studied by computer simulations. Numerical examples show that, in some cases, the proposed decoding schemes are superior to the original order statistics decoding in terms of both the bit error rate performance as well as the decoding complexity. The complexity of the order statistics based list decoding algorithms for linear block codes and binary block turbo codes (BTC) is further reduced by employing highly reliable cyclic redundancy check (CRC) bits. The results show that sending CRC bits for many segments is the most effective tecnhique in reducing the complexity. The coded cooperative diversity is compared with the conventional receiver coded diversity in terms of the pairwise error probability and the overall bit error rate (BER). The expressions for the pairwise error probabilities are obtained analytically and verified by computer simulations. The performance of the cooperative diversity is found to be strongly relay location dependent. Using the analytical as well as extensive numerical results, the geographical areas of the relay locations are obtained for small to medium signal-to-noise ratio values, such that the cooperative coded diversity outperforms the receiver coded diversity. However, for sufficiently large signal-to-noise ratio (SNR) values, or if the path-loss attenuations are not considered, then the receiver coded diversity always outperforms the cooperative coded diversity. The obtained results have important implications on the deployment of the next generation cellular systems supporting the cooperative as well as the receiver diversity
A STUDY OF ERASURE CORRECTING CODES
This work focus on erasure codes, particularly those that of high performance,
and the related decoding algorithms, especially with low
computational complexity. The work is composed of different pieces,
but the main components are developed within the following two main
themes.
Ideas of message passing are applied to solve the erasures after the
transmission. Efficient matrix-representation of the belief propagation
(BP) decoding algorithm on the BEG is introduced as the recovery
algorithm. Gallager's bit-flipping algorithm are further developed
into the guess and multi-guess algorithms especially for the
application to recover the unsolved erasures after the recovery algorithm.
A novel maximum-likelihood decoding algorithm, the In-place
algorithm, is proposed with a reduced computational complexity. A
further study on the marginal number of correctable erasures by the
In-place algoritinn determines a lower bound of the average number
of correctable erasures. Following the spirit in search of the most likable
codeword based on the received vector, we propose a new branch-evaluation-
search-on-the-code-tree (BESOT) algorithm, which is powerful
enough to approach the ML performance for all linear block
codes.
To maximise the recovery capability of the In-place algorithm in
network transmissions, we propose the product packetisation structure
to reconcile the computational complexity of the In-place algorithm.
Combined with the proposed product packetisation structure,
the computational complexity is less than the quadratic complexity
bound. We then extend this to application of the Rayleigh fading
channel to solve the errors and erasures. By concatenating an outer
code, such as BCH codes, the product-packetised RS codes have the
performance of the hard-decision In-place algorithm significantly better
than that of the soft-decision iterative algorithms on optimally
designed LDPC codes
A STUDY OF LINEAR ERROR CORRECTING CODES
Since Shannon's ground-breaking work in 1948, there have been two main development streams
of channel coding in approaching the limit of communication channels, namely classical coding
theory which aims at designing codes with large minimum Hamming distance and probabilistic
coding which places the emphasis on low complexity probabilistic decoding using long codes built
from simple constituent codes. This work presents some further investigations in these two channel
coding development streams.
Low-density parity-check (LDPC) codes form a class of capacity-approaching codes with sparse
parity-check matrix and low-complexity decoder Two novel methods of constructing algebraic binary
LDPC codes are presented. These methods are based on the theory of cyclotomic cosets, idempotents
and Mattson-Solomon polynomials, and are complementary to each other. The two methods
generate in addition to some new cyclic iteratively decodable codes, the well-known Euclidean and
projective geometry codes. Their extension to non binary fields is shown to be straightforward.
These algebraic cyclic LDPC codes, for short block lengths, converge considerably well under iterative
decoding. It is also shown that for some of these codes, maximum likelihood performance may
be achieved by a modified belief propagation decoder which uses a different subset of 7^ codewords
of the dual code for each iteration.
Following a property of the revolving-door combination generator, multi-threaded minimum
Hamming distance computation algorithms are developed. Using these algorithms, the previously
unknown, minimum Hamming distance of the quadratic residue code for prime 199 has been evaluated.
In addition, the highest minimum Hamming distance attainable by all binary cyclic codes
of odd lengths from 129 to 189 has been determined, and as many as 901 new binary linear codes
which have higher minimum Hamming distance than the previously considered best known linear
code have been found.
It is shown that by exploiting the structure of circulant matrices, the number of codewords
required, to compute the minimum Hamming distance and the number of codewords of a given
Hamming weight of binary double-circulant codes based on primes, may be reduced. A means
of independently verifying the exhaustively computed number of codewords of a given Hamming
weight of these double-circulant codes is developed and in coiyunction with this, it is proved that
some published results are incorrect and the correct weight spectra are presented. Moreover, it is
shown that it is possible to estimate the minimum Hamming distance of this family of prime-based
double-circulant codes.
It is shown that linear codes may be efficiently decoded using the incremental correlation Dorsch
algorithm. By extending this algorithm, a list decoder is derived and a novel, CRC-less error detection
mechanism that offers much better throughput and performance than the conventional ORG
scheme is described. Using the same method it is shown that the performance of conventional CRC
scheme may be considerably enhanced. Error detection is an integral part of an incremental redundancy
communications system and it is shown that sequences of good error correction codes,
suitable for use in incremental redundancy communications systems may be obtained using the
Constructions X and XX. Examples are given and their performances presented in comparison to
conventional CRC schemes
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
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