7,844 research outputs found
Low-Density Parity-Check Codes From Transversal Designs With Improved Stopping Set Distributions
This paper examines the construction of low-density parity-check (LDPC) codes
from transversal designs based on sets of mutually orthogonal Latin squares
(MOLS). By transferring the concept of configurations in combinatorial designs
to the level of Latin squares, we thoroughly investigate the occurrence and
avoidance of stopping sets for the arising codes. Stopping sets are known to
determine the decoding performance over the binary erasure channel and should
be avoided for small sizes. Based on large sets of simple-structured MOLS, we
derive powerful constraints for the choice of suitable subsets, leading to
improved stopping set distributions for the corresponding codes. We focus on
LDPC codes with column weight 4, but the results are also applicable for the
construction of codes with higher column weights. Finally, we show that a
subclass of the presented codes has quasi-cyclic structure which allows
low-complexity encoding.Comment: 11 pages; to appear in "IEEE Transactions on Communications
The problem with the SURF scheme
There is a serious problem with one of the assumptions made in the security
proof of the SURF scheme. This problem turns out to be easy in the regime of
parameters needed for the SURF scheme to work.
We give afterwards the old version of the paper for the reader's convenience.Comment: Warning : we found a serious problem in the security proof of the
SURF scheme. We explain this problem here and give the old version of the
paper afterward
Wave: A New Family of Trapdoor One-Way Preimage Sampleable Functions Based on Codes
We present here a new family of trapdoor one-way Preimage Sampleable
Functions (PSF) based on codes, the Wave-PSF family. The trapdoor function is
one-way under two computational assumptions: the hardness of generic decoding
for high weights and the indistinguishability of generalized -codes.
Our proof follows the GPV strategy [GPV08]. By including rejection sampling, we
ensure the proper distribution for the trapdoor inverse output. The domain
sampling property of our family is ensured by using and proving a variant of
the left-over hash lemma. We instantiate the new Wave-PSF family with ternary
generalized -codes to design a "hash-and-sign" signature scheme which
achieves existential unforgeability under adaptive chosen message attacks
(EUF-CMA) in the random oracle model. For 128 bits of classical security,
signature sizes are in the order of 15 thousand bits, the public key size in
the order of 4 megabytes, and the rejection rate is limited to one rejection
every 10 to 12 signatures.Comment: arXiv admin note: text overlap with arXiv:1706.0806
Absorbing Set Analysis and Design of LDPC Codes from Transversal Designs over the AWGN Channel
In this paper we construct low-density parity-check (LDPC) codes from
transversal designs with low error-floors over the additive white Gaussian
noise (AWGN) channel. The constructed codes are based on transversal designs
that arise from sets of mutually orthogonal Latin squares (MOLS) with cyclic
structure. For lowering the error-floors, our approach is twofold: First, we
give an exhaustive classification of so-called absorbing sets that may occur in
the factor graphs of the given codes. These purely combinatorial substructures
are known to be the main cause of decoding errors in the error-floor region
over the AWGN channel by decoding with the standard sum-product algorithm
(SPA). Second, based on this classification, we exploit the specific structure
of the presented codes to eliminate the most harmful absorbing sets and derive
powerful constraints for the proper choice of code parameters in order to
obtain codes with an optimized error-floor performance.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1306.511
On the parameters of extended primitive cyclic codes and the related designs
Very recently, Heng et al. studied a family of extended primitive cyclic
codes. It was shown that the supports of all codewords with any fixed nonzero
Hamming weight of this code supporting 2-designs. In this paper, we study this
family of extended primitive cyclic codes in more details. The weight
distribution is determined. The parameters of the related -designs are also
given. Moreover, we prove that the codewords with minimum Hamming weight
supporting 3-designs, which gives an affirmative solution to Heng's conjecture
On multi-user EXIT chart analysis aided turbo-detected MBER beamforming designs
Abstract—This paper studies the mutual information transfer characteristics of a novel iterative soft interference cancellation (SIC) aided beamforming receiver communicating over both additive white Gaussian noise (AWGN) and multipath slow fading channels. Based on the extrinsic information transfer (EXIT) chart technique, we investigate the convergence behavior of an iterative minimum bit error rate (MBER) multiuser detection (MUD) scheme as a function of both the system parameters and channel conditions in comparison to the SIC aided minimum mean square error (SIC-MMSE) MUD. Our simulation results show that the EXIT chart analysis is sufficiently accurate for the MBER MUD. Quantitatively, a two-antenna system was capable of supporting up to K=6 users at Eb/N0=3dB, even when their angular separation was relatively low, potentially below 20?. Index Terms—Minimum bit error rate, beamforming, multiuser detection, soft interference cancellation, iterative processing, EXIT chart
The Subfield Codes of Some Few-Weight Linear Codes
Subfield codes of linear codes over finite fields have recently received a
lot of attention, as some of these codes are optimal and have applications in
secrete sharing, authentication codes and association schemes. In this paper,
the -ary subfield codes of six different families of
linear codes are presented, respectively. The parameters and
weight distribution of the subfield codes and their punctured codes
are explicitly determined. The parameters of the duals of
these codes are also studied. Some of the resultant -ary codes
and their dual codes are optimal
and some have the best known parameters. The parameters and weight enumerators
of the first two families of linear codes are also settled,
among which the first family is an optimal two-weight linear code meeting the
Griesmer bound, and the dual codes of these two families are almost MDS codes.
As a byproduct of this paper, a family of quaternary
Hermitian self-dual code are obtained with . As an application,
several infinite families of 2-designs and 3-designs are also constructed with
three families of linear codes of this paper.Comment: arXiv admin note: text overlap with arXiv:1804.06003,
arXiv:2207.07262 by other author
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