417 research outputs found
A Novel Stochastic Decoding of LDPC Codes with Quantitative Guarantees
Low-density parity-check codes, a class of capacity-approaching linear codes,
are particularly recognized for their efficient decoding scheme. The decoding
scheme, known as the sum-product, is an iterative algorithm consisting of
passing messages between variable and check nodes of the factor graph. The
sum-product algorithm is fully parallelizable, owing to the fact that all
messages can be update concurrently. However, since it requires extensive
number of highly interconnected wires, the fully-parallel implementation of the
sum-product on chips is exceedingly challenging. Stochastic decoding
algorithms, which exchange binary messages, are of great interest for
mitigating this challenge and have been the focus of extensive research over
the past decade. They significantly reduce the required wiring and
computational complexity of the message-passing algorithm. Even though
stochastic decoders have been shown extremely effective in practice, the
theoretical aspect and understanding of such algorithms remains limited at
large. Our main objective in this paper is to address this issue. We first
propose a novel algorithm referred to as the Markov based stochastic decoding.
Then, we provide concrete quantitative guarantees on its performance for
tree-structured as well as general factor graphs. More specifically, we provide
upper-bounds on the first and second moments of the error, illustrating that
the proposed algorithm is an asymptotically consistent estimate of the
sum-product algorithm. We also validate our theoretical predictions with
experimental results, showing we achieve comparable performance to other
practical stochastic decoders.Comment: This paper has been submitted to IEEE Transactions on Information
Theory on May 24th 201
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
A Scaling Law to Predict the Finite-Length Performance of Spatially-Coupled LDPC Codes
Spatially-coupled LDPC codes are known to have excellent asymptotic
properties. Much less is known regarding their finite-length performance. We
propose a scaling law to predict the error probability of finite-length
spatially-coupled ensembles when transmission takes place over the binary
erasure channel. We discuss how the parameters of the scaling law are connected
to fundamental quantities appearing in the asymptotic analysis of these
ensembles and we verify that the predictions of the scaling law fit well to the
data derived from simulations over a wide range of parameters. The ultimate
goal of this line of research is to develop analytic tools for the design of
spatially-coupled LDPC codes under practical constraints
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