1,762 research outputs found
Parallel pivoting combined with parallel reduction
Parallel algorithms for triangularization of large, sparse, and unsymmetric matrices are presented. The method combines the parallel reduction with a new parallel pivoting technique, control over generations of fill-ins and a check for numerical stability, all done in parallel with the work being distributed over the active processes. The parallel technique uses the compatibility relation between pivots to identify parallel pivot candidates and uses the Markowitz number of pivots to minimize fill-in. This technique is not a preordering of the sparse matrix and is applied dynamically as the decomposition proceeds
Design and Analysis of Time-Invariant SC-LDPC Convolutional Codes With Small Constraint Length
In this paper, we deal with time-invariant spatially coupled low-density
parity-check convolutional codes (SC-LDPC-CCs). Classic design approaches
usually start from quasi-cyclic low-density parity-check (QC-LDPC) block codes
and exploit suitable unwrapping procedures to obtain SC-LDPC-CCs. We show that
the direct design of the SC-LDPC-CCs syndrome former matrix or, equivalently,
the symbolic parity-check matrix, leads to codes with smaller syndrome former
constraint lengths with respect to the best solutions available in the
literature. We provide theoretical lower bounds on the syndrome former
constraint length for the most relevant families of SC-LDPC-CCs, under
constraints on the minimum length of cycles in their Tanner graphs. We also
propose new code design techniques that approach or achieve such theoretical
limits.Comment: 30 pages, 5 figures, accepted for publication in IEEE Transactions on
Communication
Efficient Linear Programming Decoding of HDPC Codes
We propose several improvements for Linear Programming (LP) decoding
algorithms for High Density Parity Check (HDPC) codes. First, we use the
automorphism groups of a code to create parity check matrix diversity and to
generate valid cuts from redundant parity checks. Second, we propose an
efficient mixed integer decoder utilizing the branch and bound method. We
further enhance the proposed decoders by removing inactive constraints and by
adapting the parity check matrix prior to decoding according to the channel
observations. Based on simulation results the proposed decoders achieve near-ML
performance with reasonable complexity.Comment: Submitted to the IEEE Transactions on Communications, November 200
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