603 research outputs found
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
Noisy Gradient Descent Bit-Flip Decoding for LDPC Codes
A modified Gradient Descent Bit Flipping (GDBF) algorithm is proposed for
decoding Low Density Parity Check (LDPC) codes on the binary-input additive
white Gaussian noise channel. The new algorithm, called Noisy GDBF (NGDBF),
introduces a random perturbation into each symbol metric at each iteration. The
noise perturbation allows the algorithm to escape from undesirable local
maxima, resulting in improved performance. A combination of heuristic
improvements to the algorithm are proposed and evaluated. When the proposed
heuristics are applied, NGDBF performs better than any previously reported GDBF
variant, and comes within 0.5 dB of the belief propagation algorithm for
several tested codes. Unlike other previous GDBF algorithms that provide an
escape from local maxima, the proposed algorithm uses only local, fully
parallelizable operations and does not require computing a global objective
function or a sort over symbol metrics, making it highly efficient in
comparison. The proposed NGDBF algorithm requires channel state information
which must be obtained from a signal to noise ratio (SNR) estimator.
Architectural details are presented for implementing the NGDBF algorithm.
Complexity analysis and optimizations are also discussed.Comment: 16 pages, 22 figures, 2 table
Wave-like Decoding of Tail-biting Spatially Coupled LDPC Codes Through Iterative Demapping
For finite coupling lengths, terminated spatially coupled low-density
parity-check (SC-LDPC) codes show a non-negligible rate-loss. In this paper, we
investigate if this rate loss can be mitigated by tail-biting SC-LDPC codes in
conjunction with iterative demapping of higher order modulation formats.
Therefore, we examine the BP threshold of different coupled and uncoupled
ensembles. A comparison between the decoding thresholds approximated by EXIT
charts and the density evolution results of the coupled and uncoupled ensemble
is given. We investigate the effect and potential of different labelings for
such a set-up using per-bit EXIT curves, and exemplify the method for a 16-QAM
system, e.g., using set partitioning labelings. A hybrid mapping is proposed,
where different sub-blocks use different labelings in order to further optimize
the decoding thresholds of tail-biting codes, while the computational
complexity overhead through iterative demapping remains small.Comment: presentat at the International Symposium on Turbo Codes & Iterative
Information Processing (ISTC), Brest, Sept. 201
Capacity-Achieving Codes with Bounded Graphical Complexity on Noisy Channels
We introduce a new family of concatenated codes with an outer low-density
parity-check (LDPC) code and an inner low-density generator matrix (LDGM) code,
and prove that these codes can achieve capacity under any memoryless
binary-input output-symmetric (MBIOS) channel using maximum-likelihood (ML)
decoding with bounded graphical complexity, i.e., the number of edges per
information bit in their graphical representation is bounded. In particular, we
also show that these codes can achieve capacity on the binary erasure channel
(BEC) under belief propagation (BP) decoding with bounded decoding complexity
per information bit per iteration for all erasure probabilities in (0, 1). By
deriving and analyzing the average weight distribution (AWD) and the
corresponding asymptotic growth rate of these codes with a rate-1 inner LDGM
code, we also show that these codes achieve the Gilbert-Varshamov bound with
asymptotically high probability. This result can be attributed to the presence
of the inner rate-1 LDGM code, which is demonstrated to help eliminate high
weight codewords in the LDPC code while maintaining a vanishingly small amount
of low weight codewords.Comment: 17 pages, 2 figures. This paper is to be presented in the 43rd Annual
Allerton Conference on Communication, Control and Computing, Monticello, IL,
USA, Sept. 28-30, 200
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