92,151 research outputs found
Low-Complexity LP Decoding of Nonbinary Linear Codes
Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has
attracted much attention in the research community in the past few years. LP
decoding has been derived for binary and nonbinary linear codes. However, the
most important problem with LP decoding for both binary and nonbinary linear
codes is that the complexity of standard LP solvers such as the simplex
algorithm remains prohibitively large for codes of moderate to large block
length. To address this problem, two low-complexity LP (LCLP) decoding
algorithms for binary linear codes have been proposed by Vontobel and Koetter,
henceforth called the basic LCLP decoding algorithm and the subgradient LCLP
decoding algorithm.
In this paper, we generalize these LCLP decoding algorithms to nonbinary
linear codes. The computational complexity per iteration of the proposed
nonbinary LCLP decoding algorithms scales linearly with the block length of the
code. A modified BCJR algorithm for efficient check-node calculations in the
nonbinary basic LCLP decoding algorithm is also proposed, which has complexity
linear in the check node degree.
Several simulation results are presented for nonbinary LDPC codes defined
over Z_4, GF(4), and GF(8) using quaternary phase-shift keying and
8-phase-shift keying, respectively, over the AWGN channel. It is shown that for
some group-structured LDPC codes, the error-correcting performance of the
nonbinary LCLP decoding algorithms is similar to or better than that of the
min-sum decoding algorithm.Comment: To appear in IEEE Transactions on Communications, 201
Decoding the Golay code with Venn diagrams
A decoding algorithm, based on Venn diagrams, for decoding the [23, 12, 7] Golay code is presented. The decoding algorithm is based on the design properties of the parity sets of the code. As for other decoding algorithms for the Golay code, decoding can be easily done by hand
On Decoding Schemes for the MDPC-McEliece Cryptosystem
Recently, it has been shown how McEliece public-key cryptosystems based on
moderate-density parity-check (MDPC) codes allow for very compact keys compared
to variants based on other code families. In this paper, classical (iterative)
decoding schemes for MPDC codes are considered. The algorithms are analyzed
with respect to their error-correction capability as well as their resilience
against a recently proposed reaction-based key-recovery attack on a variant of
the MDPC-McEliece cryptosystem by Guo, Johansson and Stankovski (GJS). New
message-passing decoding algorithms are presented and analyzed. Two proposed
decoding algorithms have an improved error-correction performance compared to
existing hard-decision decoding schemes and are resilient against the GJS
reaction-based attack for an appropriate choice of the algorithm's parameters.
Finally, a modified belief propagation decoding algorithm that is resilient
against the GJS reaction-based attack is presented
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