100 research outputs found
Variations of the McEliece Cryptosystem
Two variations of the McEliece cryptosystem are presented. The first one is
based on a relaxation of the column permutation in the classical McEliece
scrambling process. This is done in such a way that the Hamming weight of the
error, added in the encryption process, can be controlled so that efficient
decryption remains possible. The second variation is based on the use of
spatially coupled moderate-density parity-check codes as secret codes. These
codes are known for their excellent error-correction performance and allow for
a relatively low key size in the cryptosystem. For both variants the security
with respect to known attacks is discussed
Compact QC-LDPC Block and SC-LDPC Convolutional Codes for Low-Latency Communications
Low decoding latency and complexity are two important requirements of channel
codes used in many applications, like machine-to-machine communications. In
this paper, we show how these requirements can be fulfilled by using some
special quasi-cyclic low-density parity-check block codes and spatially coupled
low-density parity-check convolutional codes that we denote as compact. They
are defined by parity-check matrices designed according to a recent approach
based on sequentially multiplied columns. This method allows obtaining codes
with girth up to 12. Many numerical examples of practical codes are provided.Comment: 5 pages, 1 figure, presented at IEEE PIMRC 201
A mathematical tool for constructing parametrizable spatially-coupled LDPC codes with cyclic structure and large girth
Spatially-coupled low-density parity-check codes (SC-LDPC) have been shown to be superior in performance than LDPC block codes for both communication and storage systems. Several heuristic construction methods for these codes have been proposed in the literature, but they allow the construction of SC-LDPC codes for only specific nodedegrees, short code length and lead to encoders/decoders with non-parametrizable complex architectures. In this work we construct a mathematical tool for generating SC-LDPC codes with arbitrary node-degrees, girth of at least six and a parity-matrix with cyclic structure. The generated codes satisfy some minimum communication performance requirements which can be previously determined and can they can also be encoded/decoded with reduced-complexity parametrizable hardware architectures. An encoder architecture with reduced memory size and reduced-complexity, known as partial-syndrome based encoder, was implemented in software and the code encodability was verified. The partial-syndrome encoder structure proposed in the literature has constrained code rate and a modified SC-LDPC code was implemented, allowing the generated codes to be encoded with the partial-syndrome encoder architecture for arbitrary rates. A reduced-complexity decoder known as window decoder was implemented in software and the code decodability was also verified.Códigos Spatially-coupled low-density parity-check (SC-LDPC) têm apresentado melhor performance do que LDPC block codes, tanto em sistemas de comunicação quanto de armazenamento. Diversos métodos heurísticos de construção para estes códigos têm sido propostos na literatura, os quais possibilitam a obtenção de códigos SC-LDPC com específicos node-degrees, pequenos comprimentos de código e necessitam codificadores/decodificadores de arquitetura complexa não-parametrizável. Neste trabalho, construiu-se uma ferramenta matemática para a geração de códigos SC-LDPC com node-degrees arbitrários, girth de no mínimo seis e matriz de paridade com estrutura cíclica. Os códigos gerados satisfazem requisitos mínimos de performance de comunicação que podem ser previamente estabelecidos e podem ser codificados/decodificados por arquiteturas de hardware parametrizáveis de complexidade reduzida. Implementou-se em software um codificador de arquitetura parametrizável com tamanho de memória reduzido e baixa complexidade, conhecido como codificador baseado em partial syndrome, e verificou-se a codificação dos códigos construídos. As arquiteturas para codificadores do tipo partial-syndrome encontradas na literatura possuem taxas de codificação não arbitrárias e por isso, modificou-se os códigos SC-LDPC construídos, permitindo que os códigos gerados possam ser codificados com o mesmo codificador do tipo partial-syndrome para taxas de codificação arbitrárias. Implementou-se em software um decodificador de complexidade reduzida, conhecido como window decoder, e verificou-se a convergência dos códigos SC-LDPC construídos
Hierarchical and High-Girth QC LDPC Codes
We present a general approach to designing capacity-approaching high-girth
low-density parity-check (LDPC) codes that are friendly to hardware
implementation. Our methodology starts by defining a new class of
"hierarchical" quasi-cyclic (HQC) LDPC codes that generalizes the structure of
quasi-cyclic (QC) LDPC codes. Whereas the parity check matrices of QC LDPC
codes are composed of circulant sub-matrices, those of HQC LDPC codes are
composed of a hierarchy of circulant sub-matrices that are in turn constructed
from circulant sub-matrices, and so on, through some number of levels. We show
how to map any class of codes defined using a protograph into a family of HQC
LDPC codes. Next, we present a girth-maximizing algorithm that optimizes the
degrees of freedom within the family of codes to yield a high-girth HQC LDPC
code. Finally, we discuss how certain characteristics of a code protograph will
lead to inevitable short cycles, and show that these short cycles can be
eliminated using a "squashing" procedure that results in a high-girth QC LDPC
code, although not a hierarchical one. We illustrate our approach with designed
examples of girth-10 QC LDPC codes obtained from protographs of one-sided
spatially-coupled codes.Comment: Submitted to IEEE Transactions on Information THeor
The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing
and protecting fragile qubits against the undesirable effects of quantum
decoherence. Similar to classical codes, hashing bound approaching QECCs may be
designed by exploiting a concatenated code structure, which invokes iterative
decoding. Therefore, in this paper we provide an extensive step-by-step
tutorial for designing EXtrinsic Information Transfer (EXIT) chart aided
concatenated quantum codes based on the underlying quantum-to-classical
isomorphism. These design lessons are then exemplified in the context of our
proposed Quantum Irregular Convolutional Code (QIRCC), which constitutes the
outer component of a concatenated quantum code. The proposed QIRCC can be
dynamically adapted to match any given inner code using EXIT charts, hence
achieving a performance close to the hashing bound. It is demonstrated that our
QIRCC-based optimized design is capable of operating within 0.4 dB of the noise
limit
Spatially Coupled Codes and Optical Fiber Communications: An Ideal Match?
In this paper, we highlight the class of spatially coupled codes and discuss
their applicability to long-haul and submarine optical communication systems.
We first demonstrate how to optimize irregular spatially coupled LDPC codes for
their use in optical communications with limited decoding hardware complexity
and then present simulation results with an FPGA-based decoder where we show
that very low error rates can be achieved and that conventional block-based
LDPC codes can be outperformed. In the second part of the paper, we focus on
the combination of spatially coupled LDPC codes with different demodulators and
detectors, important for future systems with adaptive modulation and for
varying channel characteristics. We demonstrate that SC codes can be employed
as universal, channel-agnostic coding schemes.Comment: Invited paper to be presented in the special session on "Signal
Processing, Coding, and Information Theory for Optical Communications" at
IEEE SPAWC 201
Efficient Search of Compact QC-LDPC and SC-LDPC Convolutional Codes with Large Girth
We propose a low-complexity method to find quasi-cyclic low-density
parity-check block codes with girth 10 or 12 and shorter length than those
designed through classical approaches. The method is extended to time-invariant
spatially coupled low-density parity-check convolutional codes, permitting to
achieve small syndrome former constraint lengths. Several numerical examples
are given to show its effectiveness.Comment: 4 pages, 3 figures, 1 table, accepted for publication in IEEE
Communications Letter
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