3,382 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
Discriminative Recurrent Sparse Auto-Encoders
We present the discriminative recurrent sparse auto-encoder model, comprising
a recurrent encoder of rectified linear units, unrolled for a fixed number of
iterations, and connected to two linear decoders that reconstruct the input and
predict its supervised classification. Training via
backpropagation-through-time initially minimizes an unsupervised sparse
reconstruction error; the loss function is then augmented with a discriminative
term on the supervised classification. The depth implicit in the
temporally-unrolled form allows the system to exhibit all the power of deep
networks, while substantially reducing the number of trainable parameters.
From an initially unstructured network the hidden units differentiate into
categorical-units, each of which represents an input prototype with a
well-defined class; and part-units representing deformations of these
prototypes. The learned organization of the recurrent encoder is hierarchical:
part-units are driven directly by the input, whereas the activity of
categorical-units builds up over time through interactions with the part-units.
Even using a small number of hidden units per layer, discriminative recurrent
sparse auto-encoders achieve excellent performance on MNIST.Comment: Added clarifications suggested by reviewers. 15 pages, 10 figure
Orthogonal Multiple Access with Correlated Sources: Feasible Region and Pragmatic Schemes
In this paper, we consider orthogonal multiple access coding schemes, where
correlated sources are encoded in a distributed fashion and transmitted,
through additive white Gaussian noise (AWGN) channels, to an access point (AP).
At the AP, component decoders, associated with the source encoders, iteratively
exchange soft information by taking into account the source correlation. The
first goal of this paper is to investigate the ultimate achievable performance
limits in terms of a multi-dimensional feasible region in the space of channel
parameters, deriving insights on the impact of the number of sources. The
second goal is the design of pragmatic schemes, where the sources use
"off-the-shelf" channel codes. In order to analyze the performance of given
coding schemes, we propose an extrinsic information transfer (EXIT)-based
approach, which allows to determine the corresponding multi-dimensional
feasible regions. On the basis of the proposed analytical framework, the
performance of pragmatic coded schemes, based on serially concatenated
convolutional codes (SCCCs), is discussed
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