296 research outputs found
Threshold Analysis of Non-Binary Spatially-Coupled LDPC Codes with Windowed Decoding
In this paper we study the iterative decoding threshold performance of
non-binary spatially-coupled low-density parity-check (NB-SC-LDPC) code
ensembles for both the binary erasure channel (BEC) and the binary-input
additive white Gaussian noise channel (BIAWGNC), with particular emphasis on
windowed decoding (WD). We consider both (2,4)-regular and (3,6)-regular
NB-SC-LDPC code ensembles constructed using protographs and compute their
thresholds using protograph versions of NB density evolution and NB extrinsic
information transfer analysis. For these code ensembles, we show that WD of
NB-SC-LDPC codes, which provides a significant decrease in latency and
complexity compared to decoding across the entire parity-check matrix, results
in a negligible decrease in the near-capacity performance for a sufficiently
large window size W on both the BEC and the BIAWGNC. Also, we show that
NB-SC-LDPC code ensembles exhibit gains in the WD threshold compared to the
corresponding block code ensembles decoded across the entire parity-check
matrix, and that the gains increase as the finite field size q increases.
Moreover, from the viewpoint of decoding complexity, we see that (3,6)-regular
NB-SC-LDPC codes are particularly attractive due to the fact that they achieve
near-capacity thresholds even for small q and W.Comment: 6 pages, 8 figures; submitted to 2014 IEEE International Symposium 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
Proving Threshold Saturation for Nonbinary SC-LDPC Codes on the Binary Erasure Channel
We analyze nonbinary spatially-coupled low-density parity-check (SC-LDPC)
codes built on the general linear group for transmission over the binary
erasure channel. We prove threshold saturation of the belief propagation
decoding to the potential threshold, by generalizing the proof technique based
on potential functions recently introduced by Yedla et al.. The existence of
the potential function is also discussed for a vector sparse system in the
general case, and some existence conditions are developed. We finally give
density evolution and simulation results for several nonbinary SC-LDPC code
ensembles.Comment: in Proc. 2014 XXXIth URSI General Assembly and Scientific Symposium,
URSI GASS, Beijing, China, August 16-23, 2014. Invited pape
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