3,943 research outputs found
Novel irregular LDPC codes and their application to iterative detection of MIMO systems
Low-density parity-check (LDPC) codes are among the best performing error correction codes currently known.
For higher performing irregular LDPC codes, degree distributions have been found which produce codes with optimum performance in the infinite block length case. Significant performance degradation is seen at more practical short block lengths. A significant focus in the search for practical LDPC codes is to find a construction method which minimises this reduction in performance as codes approach short lengths.
In this work, a novel irregular LDPC code is proposed which makes use of the SPA decoder at the design stage in order to make the best choice of edge placement with respect to iterative decoding performance in the presence of noise. This method, a modification of the progressive edge growth (PEG) algorithm for edge placement in parity-check matrix (PCM) construction is named the DOPEG algorithm. The DOPEG design algorithm is highly flexible in that the decoder optimisation stage may be applied to any modification or extension of the original PEG algorithm with relative ease. To illustrate this fact, the decoder optimisation step was applied to the IPEG modification to the PEG algorithm, which produces codes with comparatively excellent performance. This extension to the DOPEG is called the DOIPEG.
A spatially multiplexed coded iteratively detected and decoded multiple-input multiple-output (MIMO) system is then considered. The MIMO system to be investigated is developed through theory and a number of results are presented which illustrate its performance characteristics. The novel DOPEG code is tested for the MIMO system under consideration and a significant performance gain is achieved
Deriving Good LDPC Convolutional Codes from LDPC Block Codes
Low-density parity-check (LDPC) convolutional codes are capable of achieving
excellent performance with low encoding and decoding complexity. In this paper
we discuss several graph-cover-based methods for deriving families of
time-invariant and time-varying LDPC convolutional codes from LDPC block codes
and show how earlier proposed LDPC convolutional code constructions can be
presented within this framework. Some of the constructed convolutional codes
significantly outperform the underlying LDPC block codes. We investigate some
possible reasons for this "convolutional gain," and we also discuss the ---
mostly moderate --- decoder cost increase that is incurred by going from LDPC
block to LDPC convolutional codes.Comment: Submitted to IEEE Transactions on Information Theory, April 2010;
revised August 2010, revised November 2010 (essentially final version).
(Besides many small changes, the first and second revised versions contain
corrected entries in Tables I and II.
Lowering the Error Floor of LDPC Codes Using Cyclic Liftings
Cyclic liftings are proposed to lower the error floor of low-density
parity-check (LDPC) codes. The liftings are designed to eliminate dominant
trapping sets of the base code by removing the short cycles which form the
trapping sets. We derive a necessary and sufficient condition for the cyclic
permutations assigned to the edges of a cycle of length in the
base graph such that the inverse image of in the lifted graph consists of
only cycles of length strictly larger than . The proposed method is
universal in the sense that it can be applied to any LDPC code over any channel
and for any iterative decoding algorithm. It also preserves important
properties of the base code such as degree distributions, encoder and decoder
structure, and in some cases, the code rate. The proposed method is applied to
both structured and random codes over the binary symmetric channel (BSC). The
error floor improves consistently by increasing the lifting degree, and the
results show significant improvements in the error floor compared to the base
code, a random code of the same degree distribution and block length, and a
random lifting of the same degree. Similar improvements are also observed when
the codes designed for the BSC are applied to the additive white Gaussian noise
(AWGN) channel
Design of Non-Binary Quasi-Cyclic LDPC Codes by ACE Optimization
An algorithm for constructing Tanner graphs of non-binary irregular
quasi-cyclic LDPC codes is introduced. It employs a new method for selection of
edge labels allowing control over the code's non-binary ACE spectrum and
resulting in low error-floor. The efficiency of the algorithm is demonstrated
by generating good codes of short to moderate length over small fields,
outperforming codes generated by the known methods.Comment: Accepted to 2013 IEEE Information Theory Worksho
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