934 research outputs found
Low Complexity Decoding for Higher Order Punctured Trellis-Coded Modulation Over Intersymbol Interference Channels
Trellis-coded modulation (TCM) is a power and bandwidth efficient digital
transmission scheme which offers very low structural delay of the data stream.
Classical TCM uses a signal constellation of twice the cardinality compared to
an uncoded transmission with one bit of redundancy per PAM symbol, i.e.,
application of codes with rates when denotes the
cardinality of the signal constellation.
Recently published work allows rate adjustment for TCM by means of puncturing
the convolutional code (CC) on which a TCM scheme is based on.
In this paper it is shown how punctured TCM-signals transmitted over
intersymbol interference (ISI) channels can favorably be decoded. Significant
complexity reductions at only minor performance loss can be achieved by means
of reduced state sequence estimation.Comment: 4 pages, 5 figures, 3 algorithms, accepted and published at 6th
International Symposium on Communications, Control, and Signal Processing
(ISCCSP 2014
An efficient length- and rate-preserving concatenation of polar and repetition codes
We improve the method in \cite{Seidl:10} for increasing the finite-lengh
performance of polar codes by protecting specific, less reliable symbols with
simple outer repetition codes. Decoding of the scheme integrates easily in the
known successive decoding algorithms for polar codes. Overall rate and block
length remain unchanged, the decoding complexity is at most doubled. A
comparison to related methods for performance improvement of polar codes is
drawn.Comment: to be presented at International Zurich Seminar (IZS) 201
Low Complexity Decoding for Punctured Trellis-Coded Modulation Over Intersymbol Interference Channels
Classical trellis-coded modulation (TCM) as introduced by Ungerboeck in
1976/1983 uses a signal constellation of twice the cardinality compared to an
uncoded transmission with one bit of redundancy per PAM symbol, i.e.,
application of codes with rates when denotes the
cardinality of the signal constellation. The original approach therefore only
comprises integer transmission rates, i.e., , additionally, when transmitting over an intersymbol interference
(ISI) channel an optimum decoding scheme would perform equalization and
decoding of the channel code jointly. In this paper, we allow rate adjustment
for TCM by means of puncturing the convolutional code (CC) on which a TCM
scheme is based on. In this case a nontrivial mapping of the output symbols of
the CC to signal points results in a time-variant trellis. We propose an
efficient technique to integrate an ISI-channel into this trellis and show that
the computational complexity can be significantly reduced by means of a reduced
state sequence estimation (RSSE) algorithm for time-variant trellises.Comment: 4 pages, 7 pictured, accepted for 2014 International Zurich Seminar
on Communication
Punctured Trellis-Coded Modulation
In classic trellis-coded modulation (TCM) signal constellations of twice the
cardinality are applied when compared to an uncoded transmission enabling
transmission of one bit of redundancy per PAM-symbol, i.e., rates of
when denotes the cardinality of the signal
constellation. In order to support different rates, multi-dimensional (i.e.,
-dimensional) constellations had been proposed by means of
combining subsequent one- or two-dimensional modulation steps, resulting in
TCM-schemes with bit redundancy per real dimension. In
contrast, in this paper we propose to perform rate adjustment for TCM by means
of puncturing the convolutional code (CC) on which a TCM-scheme is based on. It
is shown, that due to the nontrivial mapping of the output symbols of the CC to
signal points in the case of puncturing, a modification of the corresponding
Viterbi-decoder algorithm and an optimization of the CC and the puncturing
scheme are necessary.Comment: 5 pages, 10 figures, submitted to IEEE International Symposium on
Information Theory 2013 (ISIT
The Trapping Redundancy of Linear Block Codes
We generalize the notion of the stopping redundancy in order to study the
smallest size of a trapping set in Tanner graphs of linear block codes. In this
context, we introduce the notion of the trapping redundancy of a code, which
quantifies the relationship between the number of redundant rows in any
parity-check matrix of a given code and the size of its smallest trapping set.
Trapping sets with certain parameter sizes are known to cause error-floors in
the performance curves of iterative belief propagation decoders, and it is
therefore important to identify decoding matrices that avoid such sets. Bounds
on the trapping redundancy are obtained using probabilistic and constructive
methods, and the analysis covers both general and elementary trapping sets.
Numerical values for these bounds are computed for the [2640,1320] Margulis
code and the class of projective geometry codes, and compared with some new
code-specific trapping set size estimates.Comment: 12 pages, 4 tables, 1 figure, accepted for publication in IEEE
Transactions on Information Theor
Permutation Decoding and the Stopping Redundancy Hierarchy of Cyclic and Extended Cyclic Codes
We introduce the notion of the stopping redundancy hierarchy of a linear
block code as a measure of the trade-off between performance and complexity of
iterative decoding for the binary erasure channel. We derive lower and upper
bounds for the stopping redundancy hierarchy via Lovasz's Local Lemma and
Bonferroni-type inequalities, and specialize them for codes with cyclic
parity-check matrices. Based on the observed properties of parity-check
matrices with good stopping redundancy characteristics, we develop a novel
decoding technique, termed automorphism group decoding, that combines iterative
message passing and permutation decoding. We also present bounds on the
smallest number of permutations of an automorphism group decoder needed to
correct any set of erasures up to a prescribed size. Simulation results
demonstrate that for a large number of algebraic codes, the performance of the
new decoding method is close to that of maximum likelihood decoding.Comment: 40 pages, 6 figures, 10 tables, submitted to IEEE Transactions on
Information Theor
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