198 research outputs found
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
Analysis and Design of Tuned Turbo Codes
It has been widely observed that there exists a fundamental trade-off between
the minimum (Hamming) distance properties and the iterative decoding
convergence behavior of turbo-like codes. While capacity achieving code
ensembles typically are asymptotically bad in the sense that their minimum
distance does not grow linearly with block length, and they therefore exhibit
an error floor at moderate-to-high signal to noise ratios, asymptotically good
codes usually converge further away from channel capacity. In this paper, we
introduce the concept of tuned turbo codes, a family of asymptotically good
hybrid concatenated code ensembles, where asymptotic minimum distance growth
rates, convergence thresholds, and code rates can be traded-off using two
tuning parameters, {\lambda} and {\mu}. By decreasing {\lambda}, the asymptotic
minimum distance growth rate is reduced in exchange for improved iterative
decoding convergence behavior, while increasing {\lambda} raises the asymptotic
minimum distance growth rate at the expense of worse convergence behavior, and
thus the code performance can be tuned to fit the desired application. By
decreasing {\mu}, a similar tuning behavior can be achieved for higher rate
code ensembles.Comment: Accepted for publication in IEEE Transactions on Information Theor
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
A Better Understanding of the Performance of Rate-1/2 Binary Turbo Codes that Use Odd-Even Interleavers
The effects of the odd-even constraint - as an interleaver design criterion -
on the performance of rate-1/2 binary turbo codes are revisited. According to
the current understanding, its adoption is favored because it makes the
information bits be uniformly protected, each one by its own parity bit. In
this paper, we provide instances that contradict this point of view suggesting
for a different explanation of the constraint's behavior, in terms of distance
spectrum
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 LDPC Codes for Decode-and-Forward Relaying of Two Correlated Sources over the BEC
We present a decode-and-forward transmission scheme based on
spatially-coupled low-density parity-check (SC-LDPC) codes for a network
consisting of two (possibly correlated) sources, one relay, and one
destination. The links between the nodes are modeled as binary erasure
channels. Joint source-channel coding with joint channel decoding is used to
exploit the correlation. The relay performs network coding. We derive
analytical bounds on the achievable rates for the binary erasure time-division
multiple-access relay channel with correlated sources. We then design bilayer
SC-LDPC codes and analyze their asymptotic performance for this scenario. We
prove analytically that the proposed coding scheme achieves the theoretical
limit for symmetric channel conditions and uncorrelated sources. Using density
evolution, we furthermore demonstrate that our scheme approaches the
theoretical limit also for non-symmetric channel conditions and when the
sources are correlated, and we observe the threshold saturation effect that is
typical for spatially-coupled systems. Finally, we give simulation results for
large block lengths, which validate the DE analysis.Comment: IEEE Transactions on Communications, to appea
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