55 research outputs found
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
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
Threshold Saturation for Spatially Coupled Turbo-like Codes over the Binary Erasure Channel
In this paper we prove threshold saturation for spatially coupled turbo codes
(SC-TCs) and braided convolutional codes (BCCs) over the binary erasure
channel. We introduce a compact graph representation for the ensembles of SC-TC
and BCC codes which simplifies their description and the analysis of the
message passing decoding. We demonstrate that by few assumptions in the
ensembles of these codes, it is possible to rewrite their vector recursions in
a form which places these ensembles under the category of scalar admissible
systems. This allows us to define potential functions and prove threshold
saturation using the proof technique introduced by Yedla et al..Comment: 5 pages, 3figure
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
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
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
Spatially Coupled Turbo-Like Codes
The focus of this thesis is on proposing and analyzing a powerful class of codes on graphs---with trellis constraints---that can simultaneously approach capacity and achieve very low error floor. In particular, we propose the concept of spatial coupling for turbo-like code (SC-TC) ensembles and investigate the impact of coupling on the performance of these codes. The main elements of this study can be summarized by the following four major topics. First, we considered the spatial coupling of parallel concatenated codes (PCCs), serially concatenated codes (SCCs), and hybrid concatenated codes (HCCs).We also proposed two extensions of braided convolutional codes (BCCs) to higher coupling memories. Second, we investigated the impact of coupling on the asymptotic behavior of the proposed ensembles in term of the decoding thresholds. For that, we derived the exact density evolution (DE) equations of the proposed SC-TC ensembles over the binary erasure channel. Using the DE equations, we found the thresholds of the coupled and uncoupled ensembles under belief propagation (BP) decoding for a wide range of rates. We also computed the maximum a-posteriori (MAP) thresholds of the underlying uncoupled ensembles. Our numerical results confirm that TCs have excellent MAP thresholds, and for a large enough coupling memory, the BP threshold of an SC-TC ensemble improves to the MAP threshold of the underlying TC ensemble. This phenomenon is called threshold saturation and we proved its occurrence for SC-TCs by use of a proof technique based on the potential function of the ensembles.Third, we investigated and discussed the performance of SC-TCs in the finite length regime. We proved that under certain conditions the minimum distance of an SC-TCs is either larger or equal to that of its underlying uncoupled ensemble. Based on this fact, we performed a weight enumerator (WE) analysis for the underlying uncoupled ensembles to investigate the error floor performance of the SC-TC ensembles. We computed bounds on the error rate performance and minimum distance of the TC ensembles. These bounds indicate very low error floor for SCC, HCC, and BCC ensembles, and show that for HCC, and BCC ensembles, the minimum distance grows linearly with the input block length.The results from the DE and WE analysis demonstrate that the performance of TCs benefits from spatial coupling in both waterfall and error floor regions. While uncoupled TC ensembles with close-to-capacity performance exhibit a high error floor, our results show that SC-TCs can simultaneously approach capacity and achieve very low error floor.Fourth, we proposed a unified ensemble of TCs that includes all the considered TC classes. We showed 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. This unified ensemble not only helps us to understand the connections and trade-offs between the TC ensembles but also can be considered as a bridge between TCs and generalized low-density parity check codes
Thresholds of Braided Convolutional Codes on the AWGN Channel
In this paper, we perform a threshold analysis of braided convolutional codes
(BCCs) on the additive white Gaussian noise (AWGN) channel. The decoding
thresholds are estimated by Monte-Carlo density evolution (MC-DE) techniques
and compared with approximate thresholds from an erasure channel prediction.
The results show that, with spatial coupling, the predicted thresholds are very
accurate and quickly approach capacity if the coupling memory is increased. For
uncoupled ensembles with random puncturing, the prediction can be improved with
help of the AWGN threshold of the unpunctured ensemble
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