1,026 research outputs found
On the Minimum Distance of Generalized Spatially Coupled LDPC Codes
Families of generalized spatially-coupled low-density parity-check (GSC-LDPC)
code ensembles can be formed by terminating protograph-based generalized LDPC
convolutional (GLDPCC) codes. It has previously been shown that ensembles of
GSC-LDPC codes constructed from a protograph have better iterative decoding
thresholds than their block code counterparts, and that, for large termination
lengths, their thresholds coincide with the maximum a-posteriori (MAP) decoding
threshold of the underlying generalized LDPC block code ensemble. Here we show
that, in addition to their excellent iterative decoding thresholds, ensembles
of GSC-LDPC codes are asymptotically good and have large minimum distance
growth rates.Comment: Submitted to the IEEE International Symposium on Information Theory
201
Spatially Coupled LDPC Codes Constructed from Protographs
In this paper, we construct protograph-based spatially coupled low-density
parity-check (SC-LDPC) codes by coupling together a series of L disjoint, or
uncoupled, LDPC code Tanner graphs into a single coupled chain. By varying L,
we obtain a flexible family of code ensembles with varying rates and frame
lengths that can share the same encoding and decoding architecture for
arbitrary L. We demonstrate that the resulting codes combine the best features
of optimized irregular and regular codes in one design: capacity approaching
iterative belief propagation (BP) decoding thresholds and linear growth of
minimum distance with block length. In particular, we show that, for
sufficiently large L, the BP thresholds on both the binary erasure channel
(BEC) and the binary-input additive white Gaussian noise channel (AWGNC)
saturate to a particular value significantly better than the BP decoding
threshold and numerically indistinguishable from the optimal maximum
a-posteriori (MAP) decoding threshold of the uncoupled LDPC code. When all
variable nodes in the coupled chain have degree greater than two,
asymptotically the error probability converges at least doubly exponentially
with decoding iterations and we obtain sequences of asymptotically good LDPC
codes with fast convergence rates and BP thresholds close to the Shannon limit.
Further, the gap to capacity decreases as the density of the graph increases,
opening up a new way to construct capacity achieving codes on memoryless
binary-input symmetric-output (MBS) channels with low-complexity BP decoding.Comment: Submitted to the IEEE Transactions on Information Theor
Quasi-Cyclic Asymptotically Regular LDPC Codes
Families of "asymptotically regular" LDPC block code ensembles can be formed
by terminating (J,K)-regular protograph-based LDPC convolutional codes. By
varying the termination length, we obtain a large selection of LDPC block code
ensembles with varying code rates, minimum distance that grows linearly with
block length, and capacity approaching iterative decoding thresholds, despite
the fact that the terminated ensembles are almost regular. In this paper, we
investigate the properties of the quasi-cyclic (QC) members of such an
ensemble. We show that an upper bound on the minimum Hamming distance of
members of the QC sub-ensemble can be improved by careful choice of the
component protographs used in the code construction. Further, we show that the
upper bound on the minimum distance can be improved by using arrays of
circulants in a graph cover of the protograph.Comment: To be presented at the 2010 IEEE Information Theory Workshop, Dublin,
Irelan
New Codes on Graphs Constructed by Connecting Spatially Coupled Chains
A novel code construction based on spatially coupled low-density parity-check
(SC-LDPC) codes is presented. The proposed code ensembles are described by
protographs, comprised of several protograph-based chains characterizing
individual SC-LDPC codes. We demonstrate that code ensembles obtained by
connecting appropriately chosen SC-LDPC code chains at specific points have
improved iterative decoding thresholds compared to those of single SC-LDPC
coupled chains. In addition, it is shown that the improved decoding properties
of the connected ensembles result in reduced decoding complexity required to
achieve a specific bit error probability. The constructed ensembles are also
asymptotically good, in the sense that the minimum distance grows linearly with
the block length. Finally, we show that the improved asymptotic properties of
the connected chain ensembles also translate into improved finite length
performance.Comment: Submitted to IEEE Transactions on Information Theor
Exact Free Distance and Trapping Set Growth Rates for LDPC Convolutional Codes
Ensembles of (J,K)-regular low-density parity-check convolutional (LDPCC)
codes are known to be asymptotically good, in the sense that the minimum free
distance grows linearly with the constraint length. In this paper, we use a
protograph-based analysis of terminated LDPCC codes to obtain an upper bound on
the free distance growth rate of ensembles of periodically time-varying LDPCC
codes. This bound is compared to a lower bound and evaluated numerically. It is
found that, for a sufficiently large period, the bounds coincide. This approach
is then extended to obtain bounds on the trapping set numbers, which define the
size of the smallest, non-empty trapping sets, for these asymptotically good,
periodically time-varying LDPCC code ensembles.Comment: To be presented at the 2011 IEEE International Symposium on
Information Theor
Barriers and Incentives to the Commercialization of Solar Heating and Cooling of Buildings
This paper reviews potential barriers to the widespread use of solar heating and cooling systems in residential and commercial buildings. Although solar systems have been technologically proven and are used to a limited extent today, economic, institutional, and legal barriers may slow future commercialization. Consideration of incentives which might reduce these barriers raises the question of how to evaluate alternative policy question options
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