29,570 research outputs found
On the Multiple Threshold Decoding of LDPC codes over GF(q)
We consider the decoding of LDPC codes over GF(q) with the low-complexity
majority algorithm from [1]. A modification of this algorithm with multiple
thresholds is suggested. A lower estimate on the decoding radius realized by
the new algorithm is derived. The estimate is shown to be better than the
estimate for a single threshold majority decoder. At the same time the
transition to multiple thresholds does not affect the order of complexity.Comment: 5 pages, submitted to ISIT 201
Recursive Decoding and Its Performance for Low-Rate Reed-Muller Codes
Recursive decoding techniques are considered for Reed-Muller (RM) codes of
growing length and fixed order An algorithm is designed that has
complexity of order and corrects most error patterns of weight up to
given that exceeds This
improves the asymptotic bounds known for decoding RM codes with nonexponential
complexity
Decoding of NB-LDPC codes over Subfields
The non-binary low-density parity-check (NB-LDPC) codes can offer promising
performance advantages but suffer from high decoding complexity. To tackle this
challenge, in this paper, we consider NB-LDPC codes over finite fields as codes
over \textit{subfields} as a means of reducing decoding complexity. In
particular, our approach is based on a novel method of expanding a non-binary
Tanner graph over a finite field into a graph over a subfield. This approach
offers several decoding strategies for a single NB-LDPC code, with varying
levels of performance-complexity trade-offs. Simulation results demonstrate
that in a majority of cases, performance loss is minimal when compared with the
complexity gains.Comment: This work has been submitted to the IEEE for possible publication.
Copyright may be transferred without notice, after which this version may no
longer be accessibl
Group testing schemes from codes and designs
In group testing, simple binary-output tests are designed to identify a small
number of defective items that are present in a large population of
items. Each test takes as input a group of items and produces a binary output
indicating whether the group is free of the defective items or contains one or
more of them. In this paper we study a relaxation of the combinatorial group
testing problem. A matrix is called -disjunct if it gives rise to
a nonadaptive group testing scheme with the property of identifying a uniformly
random -set of defective subjects out of a population of size with false
positive probability of an item at most . We establish a new
connection between -disjunct matrices and error correcting codes
based on the dual distance of the codes and derive estimates of the parameters
of codes that give rise to such schemes. Our methods rely on the moments of the
distance distribution of codes and inequalities for moments of sums of
independent random variables. We also provide a new connection between group
testing schemes and combinatorial designs.Comment: 18 page
p-Adic estimates of Hamming weights in Abelian codes over Galois rings
A generalization of McEliece's theorem on the p-adic valuation of Hamming weights of words in cyclic codes is proved in this paper by means of counting polynomial techniques introduced by Wilson along with a technique known as trace-averaging introduced here. The original theorem of McEliece concerned cyclic codes over prime fields. Delsarte and McEliece later extended this to Abelian codes over finite fields. Calderbank, Li, and Poonen extended McEliece's original theorem to cover cyclic codes over the rings /spl Zopf//sub 2//sup d/, Wilson strengthened their results and extended them to cyclic codes over /spl Zopf//sub p//sup d/, and Katz strengthened Wilson's results and extended them to Abelian codes over /spl Zopf//sub p//sup d/. It is natural to ask whether there is a single analogue of McEliece's theorem which correctly captures the behavior of codes over all finite fields and all rings of integers modulo prime powers. In this paper, this question is answered affirmatively: a single theorem for Abelian codes over Galois rings is presented. This theorem contains all previously mentioned results and more
Importance of Symbol Equity in Coded Modulation for Power Line Communications
The use of multiple frequency shift keying modulation with permutation codes
addresses the problem of permanent narrowband noise disturbance in a power line
communications system. In this paper, we extend this coded modulation scheme
based on permutation codes to general codes and introduce an additional new
parameter that more precisely captures a code's performance against permanent
narrowband noise. As a result, we define a new class of codes, namely,
equitable symbol weight codes, which are optimal with respect to this measure
Adaptive Decision Feedback Detection with Parallel Interference Cancellation and Constellation Constraints for Multi-Antenna Systems
In this paper, a novel low-complexity adaptive decision feedback detection
with parallel decision feedback and constellation constraints (P-DFCC) is
proposed for multiuser MIMO systems. We propose a constrained constellation map
which introduces a number of selected points served as the feedback candidates
for interference cancellation. By introducing a reliability checking, a higher
degree of freedom is introduced to refine the unreliable estimates. The P-DFCC
is followed by an adaptive receive filter to estimate the transmitted symbol.
In order to reduce the complexity of computing the filters with time-varying
MIMO channels, an adaptive recursive least squares (RLS) algorithm is employed
in the proposed P-DFCC scheme. An iterative detection and decoding (Turbo)
scheme is considered with the proposed P-DFCC algorithm. Simulations show that
the proposed technique has a complexity comparable to the conventional parallel
decision feedback detector while it obtains a performance close to the maximum
likelihood detector at a low to medium SNR range.Comment: 10 figure
Recursive List Decoding for Reed-Muller Codes
We consider recursive decoding for Reed-Muller (RM) codes and their subcodes.
Two new recursive techniques are described. We analyze asymptotic properties of
these algorithms and show that they substantially outperform other decoding
algorithms with nonexponential complexity known for RM codes. Decoding
performance is further enhanced by using intermediate code lists and
permutation procedures. For moderate lengths up to 512, near-optimum decoding
with feasible complexity is obtained
Codes for Asymmetric Limited-Magnitude Errors with Application to Multi-Level Flash Memories
Several physical effects that limit the reliability and
performance of Multilevel Flash Memories induce errors that
have low magnitudes and are dominantly asymmetric. This paper studies block codes for asymmetric limited-magnitude errors over q-ary channels. We propose code constructions and bounds for such channels when the number of errors is bounded by t and the error magnitudes are bounded by ࡁ. The constructions utilize known codes for symmetric errors, over small alphabets, to protect large-alphabet symbols from asymmetric limited-magnitude errors. The encoding and decoding of these codes are performed over the small alphabet whose size depends only on the maximum error magnitude and is independent of the alphabet size of the outer code. Moreover, the size of the codes is shown
to exceed the sizes of known codes (for related error models), and asymptotic rate-optimality results are proved. Extensions of the construction are proposed to accommodate variations on the error model and to include systematic codes as a benefit to practical implementation
Soft decision decoding of Reed-Muller codes: recursive lists
Recursive list decoding is considered for Reed-Muller (RM) codes. The
algorithm repeatedly relegates itself to the shorter RM codes by recalculating
the posterior probabilities of their symbols. Intermediate decodings are only
performed when these recalculations reach the trivial RM codes. In turn, the
updated lists of most plausible codewords are used in subsequent decodings. The
algorithm is further improved by using permutation techniques on code positions
and by eliminating the most error-prone information bits. Simulation results
show that for all RM codes of length 256 and many subcodes of length 512, these
algorithms approach maximum-likelihood (ML) performance within a margin of 0.1
dB. As a result, we present tight experimental bounds on ML performance for
these codes
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