176 research outputs found
Spatially-Coupled MacKay-Neal Codes and Hsu-Anastasopoulos Codes
Kudekar et al. recently proved that for transmission over the binary erasure
channel (BEC), spatial coupling of LDPC codes increases the BP threshold of the
coupled ensemble to the MAP threshold of the underlying LDPC codes. One major
drawback of the capacity-achieving spatially-coupled LDPC codes is that one
needs to increase the column and row weight of parity-check matrices of the
underlying LDPC codes.
It is proved, that Hsu-Anastasopoulos (HA) codes and MacKay-Neal (MN) codes
achieve the capacity of memoryless binary-input symmetric-output channels under
MAP decoding with bounded column and row weight of the parity-check matrices.
The HA codes and the MN codes are dual codes each other.
The aim of this paper is to present an empirical evidence that
spatially-coupled MN (resp. HA) codes with bounded column and row weight
achieve the capacity of the BEC. To this end, we introduce a spatial coupling
scheme of MN (resp. HA) codes. By density evolution analysis, we will show that
the resulting spatially-coupled MN (resp. HA) codes have the BP threshold close
to the Shannon limit.Comment: Corrected typos in degree distributions \nu and \mu of MN and HA
code
Fourier Domain Decoding Algorithm of Non-Binary LDPC codes for Parallel Implementation
For decoding non-binary low-density parity check (LDPC) codes,
logarithm-domain sum-product (Log-SP) algorithms were proposed for reducing
quantization effects of SP algorithm in conjunction with FFT. Since FFT is not
applicable in the logarithm domain, the computations required at check nodes in
the Log-SP algorithms are computationally intensive. What is worth, check nodes
usually have higher degree than variable nodes. As a result, most of the time
for decoding is used for check node computations, which leads to a bottleneck
effect. In this paper, we propose a Log-SP algorithm in the Fourier domain.
With this algorithm, the role of variable nodes and check nodes are switched.
The intensive computations are spread over lower-degree variable nodes, which
can be efficiently calculated in parallel. Furthermore, we develop a fast
calculation method for the estimated bits and syndromes in the Fourier domain.Comment: To appear in IEICE Trans. Fundamentals, vol.E93-A, no.11 November
201
Spatially-Coupled Precoded Rateless Codes
Raptor codes are rateless codes that achieve the capacity on the binary
erasure channels. However the maximum degree of optimal output degree
distribution is unbounded. This leads to a computational complexity problem
both at encoders and decoders. Aref and Urbanke investigated the potential
advantage of universal achieving-capacity property of proposed
spatially-coupled (SC) low-density generator matrix (LDGM) codes. However the
decoding error probability of SC-LDGM codes is bounded away from 0. In this
paper, we investigate SC-LDGM codes concatenated with SC low-density
parity-check codes. The proposed codes can be regarded as SC Hsu-Anastasopoulos
rateless codes. We derive a lower bound of the asymptotic overhead from
stability analysis for successful decoding by density evolution. The numerical
calculation reveals that the lower bound is tight. We observe that with a
sufficiently large number of information bits, the asymptotic overhead and the
decoding error rate approach 0 with bounded maximum degree
Efficient Termination of Spatially-Coupled Codes
Spatially-coupled low-density parity-check codes attract much attention due
to their capacity-achieving performance and a memory-efficient sliding-window
decoding algorithm. On the other hand, the encoder needs to solve large linear
equations to terminate the encoding process. In this paper, we propose modified
spatially-coupled codes. The modified (\dl,\dr,L) codes have less rate-loss,
i.e., higher coding rate, and have the same threshold as (\dl,\dr,L) codes
and are efficiently terminable by using an accumulator
Non-Binary LDPC Codes with Large Alphabet Size
We study LDPC codes for the channel with input and
output . The aim of this paper is to evaluate
decoding performance of -ary non-binary LDPC codes for large . We give
density evolution and decoding performance evaluation for regular non-binary
LDPC codes and spatially-coupled (SC) codes. We show the regular codes do not
achieve the capacity of the channel while SC codes do
Spatially-Coupled Precoded Rateless Codes with Bounded Degree Achieve the Capacity of BEC under BP decoding
Raptor codes are known as precoded rateless codes that achieve the capacity
of BEC. However the maximum degree of Raptor codes needs to be unbounded to
achieve the capacity. In this paper, we prove that spatially-coupled precoded
rateless codes achieve the capacity with bounded degree under BP decoding
Spatially Coupled LDPC Codes for Decode-and-Forward in Erasure Relay Channel
We consider spatially-coupled protograph-based LDPC codes for the three
terminal erasure relay channel. It is observed that BP threshold value, the
maximal erasure probability of the channel for which decoding error probability
converges to zero, of spatially-coupled codes, in particular spatially-coupled
MacKay-Neal code, is close to the theoretical limit for the relay channel.
Empirical results suggest that spatially-coupled protograph-based LDPC codes
have great potential to achieve theoretical limit of a general relay channel.Comment: 7 pages, extended version of ISIT201
Design and Performance of Rate-compatible Non-Binary LDPC Convolutional Codes
In this paper, we present a construction method of non-binary low-density
parity-check (LDPC) convolutional codes. Our construction method is an
extension of Felstroem and Zigangirov construction for non-binary LDPC
convolutional codes. The rate-compatibility of the non-binary convolutional
code is also discussed. The proposed rate-compatible code is designed from one
single mother (2,4)-regular non-binary LDPC convolutional code of rate 1/2.
Higher-rate codes are produced by puncturing the mother code and lower-rate
codes are produced by multiplicatively repeating the mother code. Simulation
results show that non-binary LDPC convolutional codes of rate 1/2 outperform
state-of-the-art binary LDPC convolutional codes with comparable constraint bit
length. Also the derived low-rate and high-rate non-binary LDPC convolutional
codes exhibit good decoding performance without loss of large gap to the
Shannon limits.Comment: 8 pages, submitted to IEICE transactio
Weight Distribution for Non-binary Cluster LDPC Code Ensemble
In this paper, we derive the average weight distributions for the irregular
non-binary cluster low-density parity-check (LDPC) code ensembles. Moreover, we
give the exponential growth rate of the average weight distribution in the
limit of large code length. We show that there exist -regular
non-binary cluster LDPC code ensembles whose normalized typical minimum
distances are strictly positive.Comment: 12pages, 6 figures, To be presented in ISIT2013, Submitted to IEICE
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