5,374 research outputs found
Deterministic and Ensemble-Based Spatially-Coupled Product Codes
Several authors have proposed spatially-coupled (or convolutional-like)
variants of product codes (PCs). In this paper, we focus on a parametrized
family of generalized PCs that recovers some of these codes (e.g., staircase
and block-wise braided codes) as special cases and study the iterative decoding
performance over the binary erasure channel. Even though our code construction
is deterministic (and not based on a randomized ensemble), we show that it is
still possible to rigorously derive the density evolution (DE) equations that
govern the asymptotic performance. The obtained DE equations are then compared
to those for a related spatially-coupled PC ensemble. In particular, we show
that there exists a family of (deterministic) braided codes that follows the
same DE equation as the ensemble, for any spatial length and coupling width.Comment: accepted at ISIT 2016, Barcelona, Spai
Approaching Capacity at High-Rates with Iterative Hard-Decision Decoding
A variety of low-density parity-check (LDPC) ensembles have now been observed
to approach capacity with message-passing decoding. However, all of them use
soft (i.e., non-binary) messages and a posteriori probability (APP) decoding of
their component codes. In this paper, we show that one can approach capacity at
high rates using iterative hard-decision decoding (HDD) of generalized product
codes. Specifically, a class of spatially-coupled GLDPC codes with BCH
component codes is considered, and it is observed that, in the high-rate
regime, they can approach capacity under the proposed iterative HDD. These
codes can be seen as generalized product codes and are closely related to
braided block codes. An iterative HDD algorithm is proposed that enables one to
analyze the performance of these codes via density evolution (DE).Comment: 22 pages, this version accepted to the IEEE Transactions on
Information Theor
Error Propagation Mitigation in Sliding Window Decoding of Braided Convolutional Codes
We investigate error propagation in sliding window decoding of braided
convolutional codes (BCCs). Previous studies of BCCs have focused on iterative
decoding thresholds, minimum distance properties, and their bit error rate
(BER) performance at small to moderate frame length. Here, we consider a
sliding window decoder in the context of large frame length or one that
continuously outputs blocks in a streaming fashion. In this case, decoder error
propagation, due to the feedback inherent in BCCs, can be a serious problem.In
order to mitigate the effects of error propagation, we propose several schemes:
a \emph{window extension algorithm} where the decoder window size can be
extended adaptively, a resynchronization mechanism where we reset the encoder
to the initial state, and a retransmission strategy where erroneously decoded
blocks are retransmitted. In addition, we introduce a soft BER stopping rule to
reduce computational complexity, and the tradeoff between performance and
complexity is examined. Simulation results show that, using the proposed window
extension algorithm, resynchronization mechanism, and retransmission strategy,
the BER performance of BCCs can be improved by up to four orders of magnitude
in the signal-to-noise ratio operating range of interest, and in addition the
soft BER stopping rule can be employed to reduce computational complexity.Comment: arXiv admin note: text overlap with arXiv:1801.0323
Braided Convolutional Codes -- A Class of Spatially Coupled Turbo-Like Codes
In this paper, we investigate the impact of spatial coupling on the
thresholds of turbo-like codes. Parallel concatenated and serially concatenated
convolutional codes as well as braided convolutional codes (BCCs) are compared
by means of an exact density evolution (DE) analysis for the binary erasure
channel (BEC). We propose two extensions of the original BCC ensemble to
improve its threshold and demonstrate that their BP thresholds approach the
maximum-a-posteriori (MAP) threshold of the uncoupled ensemble. A comparison of
the different ensembles shows that parallel concatenated ensembles can be
outperformed by both serially concatenated and BCC ensembles, although they
have the best BP thresholds in the uncoupled case.Comment: Invited paper, International Conference on Signal Processing and
Communications, SPCOM 2014, Bangalore, India, July 22-25, 201
A Unified Ensemble of Concatenated Convolutional Codes
We introduce a unified ensemble for turbo-like codes (TCs) that contains the
four main classes of TCs: parallel concatenated codes, serially concatenated
codes, hybrid concatenated codes, and braided convolutional codes. We show that
for each of the original classes of TCs, it is possible to find an equivalent
ensemble by proper selection of the design parameters in the unified ensemble.
We also derive the density evolution (DE) equations for this ensemble over the
binary erasure channel. The thresholds obtained from the DE indicate that the
TC ensembles from the unified ensemble have similar asymptotic behavior to the
original TC ensembles
Density Evolution for Deterministic Generalized Product Codes with Higher-Order Modulation
Generalized product codes (GPCs) are extensions of product codes (PCs) where
coded bits are protected by two component codes but not necessarily arranged in
a rectangular array. It has recently been shown that there exists a large class
of deterministic GPCs (including, e.g., irregular PCs, half-product codes,
staircase codes, and certain braided codes) for which the asymptotic
performance under iterative bounded-distance decoding over the binary erasure
channel (BEC) can be rigorously characterized in terms of a density evolution
analysis. In this paper, the analysis is extended to the case where
transmission takes place over parallel BECs with different erasure
probabilities. We use this model to predict the code performance in a coded
modulation setup with higher-order signal constellations. We also discuss the
design of the bit mapper that determines the allocation of the coded bits to
the modulation bits of the signal constellation.Comment: invited and accepted paper for the special session "Recent Advances
in Coding for Higher Order Modulation" at the International Symposium on
Turbo Codes & Iterative Information Processing, Brest, France, 201
Spatially Coupled Turbo Codes: Principles and Finite Length Performance
In this paper, we give an overview of spatially coupled turbo codes (SC-TCs),
the spatial coupling of parallel and serially concatenated convolutional codes,
recently introduced by the authors. For presentation purposes, we focus on
spatially coupled serially concatenated codes (SC-SCCs). We review the main
principles of SC-TCs and discuss their exact density evolution (DE) analysis on
the binary erasure channel. We also consider the construction of a family of
rate-compatible SC-SCCs with simple 4-state component encoders. For all
considered code rates, threshold saturation of the belief propagation (BP) to
the maximum a posteriori threshold of the uncoupled ensemble is demonstrated,
and it is shown that the BP threshold approaches the Shannon limit as the
coupling memory increases. Finally we give some simulation results for finite
lengths.Comment: Invited paper, IEEE Int. Symp. Wireless Communications Systems
(ISWCS), Aug. 201
Spatially Coupled Turbo Codes
In this paper, we introduce the concept of spatially coupled turbo codes
(SC-TCs), as the turbo codes counterpart of spatially coupled low-density
parity-check codes. We describe spatial coupling for both Berrou et al. and
Benedetto et al. parallel and serially concatenated codes. For the binary
erasure channel, we derive the exact density evolution (DE) equations of SC-TCs
by using the method proposed by Kurkoski et al. to compute the decoding erasure
probability of convolutional encoders. Using DE, we then analyze the asymptotic
behavior of SC-TCs. We observe that the belief propagation (BP) threshold of
SC-TCs improves with respect to that of the uncoupled ensemble and approaches
its maximum a posteriori threshold. This phenomenon is especially significant
for serially concatenated codes, whose uncoupled ensemble suffers from a poor
BP threshold.Comment: in Proc. 8th International Symposium on Turbo Codes & Iterative
Information Processing 2014, Bremen, Germany, August 2014. To appear. (The
PCC ensemble is changed with respect to the one in the previous version of
the paper. However, it gives identical thresholds
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