2,337 research outputs found
Adaptive Cut Generation Algorithm for Improved Linear Programming Decoding of Binary Linear Codes
Linear programming (LP) decoding approximates maximum-likelihood (ML)
decoding of a linear block code by relaxing the equivalent ML integer
programming (IP) problem into a more easily solved LP problem. The LP problem
is defined by a set of box constraints together with a set of linear
inequalities called "parity inequalities" that are derived from the constraints
represented by the rows of a parity-check matrix of the code and can be added
iteratively and adaptively. In this paper, we first derive a new necessary
condition and a new sufficient condition for a violated parity inequality
constraint, or "cut," at a point in the unit hypercube. Then, we propose a new
and effective algorithm to generate parity inequalities derived from certain
additional redundant parity check (RPC) constraints that can eliminate
pseudocodewords produced by the LP decoder, often significantly improving the
decoder error-rate performance. The cut-generating algorithm is based upon a
specific transformation of an initial parity-check matrix of the linear block
code. We also design two variations of the proposed decoder to make it more
efficient when it is combined with the new cut-generating algorithm. Simulation
results for several low-density parity-check (LDPC) codes demonstrate that the
proposed decoding algorithms significantly narrow the performance gap between
LP decoding and ML decoding
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
Adaptive Causal Network Coding with Feedback for Multipath Multi-hop Communications
We propose a novel multipath multi-hop adaptive and causal random linear
network coding (AC-RLNC) algorithm with forward error correction. This
algorithm generalizes our joint optimization coding solution for point-to-point
communication with delayed feedback. AC-RLNC is adaptive to the estimated
channel condition, and is causal, as the coding adjusts the retransmission
rates using a priori and posteriori algorithms. In the multipath network, to
achieve the desired throughput and delay, we propose to incorporate an adaptive
packet allocation algorithm for retransmission, across the available resources
of the paths. This approach is based on a discrete water filling algorithm,
i.e., bit-filling, but, with two desired objectives, maximize throughput and
minimize the delay. In the multipath multi-hop setting, we propose a new
decentralized balancing optimization algorithm. This balancing algorithm
minimizes the throughput degradation, caused by the variations in the channel
quality of the paths at each hop. Furthermore, to increase the efficiency, in
terms of the desired objectives, we propose a new selective recoding method at
the intermediate nodes. We derive bounds on the throughput and the mean and
maximum in order delivery delay of AC-RLNC, both in the multipath and multipath
multi-hop case. In the multipath case, we prove that in the non-asymptotic
regime, the suggested code may achieve more than 90% of the channel capacity
with zero error probability. In the multipath multi-hop case, the balancing
procedure is proven to be optimal with regards to the achieved rate. Through
simulations, we demonstrate that the performance of our adaptive and causal
approach, compared to selective repeat (SR)-ARQ protocol, is capable of gains
up to a factor two in throughput and a factor of more than three in delay
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