704 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
Performance Analysis and Design of Two Edge Type LDPC Codes for the BEC Wiretap Channel
We consider transmission over a wiretap channel where both the main channel
and the wiretapper's channel are Binary Erasure Channels (BEC). We propose a
code construction method using two edge type LDPC codes based on the coset
encoding scheme. Using a standard LDPC ensemble with a given threshold over the
BEC, we give a construction for a two edge type LDPC ensemble with the same
threshold. If the given standard LDPC ensemble has degree two variable nodes,
our construction gives rise to degree one variable nodes in the code used over
the main channel. This results in zero threshold over the main channel. In
order to circumvent this problem, we numerically optimize the degree
distribution of the two edge type LDPC ensemble. We find that the resulting
ensembles are able to perform close to the boundary of the rate-equivocation
region of the wiretap channel.
There are two performance criteria for a coding scheme used over a wiretap
channel: reliability and secrecy. The reliability measure corresponds to the
probability of decoding error for the intended receiver. This can be easily
measured using density evolution recursion. However, it is more challenging to
characterize secrecy, corresponding to the equivocation of the message for the
wiretapper. M\'easson, Montanari, and Urbanke have shown how the equivocation
can be measured for a broad range of standard LDPC ensembles for transmission
over the BEC under the point-to-point setup. By generalizing the method of
M\'easson, Montanari, and Urbanke to two edge type LDPC ensembles, we show how
the equivocation for the wiretapper can be computed. We find that relatively
simple constructions give very good secrecy performance and are close to the
secrecy capacity. However finding explicit sequences of two edge type LDPC
ensembles which achieve secrecy capacity is a more difficult problem. We pose
it as an interesting open problem.Comment: submitted to IEEE Transactions on Information Theory. Updated versio
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
Trans. Fundamental
Multiplicatively Repeated Non-Binary LDPC Codes
We propose non-binary LDPC codes concatenated with multiplicative repetition
codes. By multiplicatively repeating the (2,3)-regular non-binary LDPC mother
code of rate 1/3, we construct rate-compatible codes of lower rates 1/6, 1/9,
1/12,... Surprisingly, such simple low-rate non-binary LDPC codes outperform
the best low-rate binary LDPC codes so far. Moreover, we propose the decoding
algorithm for the proposed codes, which can be decoded with almost the same
computational complexity as that of the mother code.Comment: To appear in IEEE Transactions on Information Theor
Stability of Iterative Decoding of Multi-Edge Type Doubly-Generalized LDPC Codes Over the BEC
Using the EXIT chart approach, a necessary and sufficient condition is
developed for the local stability of iterative decoding of multi-edge type
(MET) doubly-generalized low-density parity-check (D-GLDPC) code ensembles. In
such code ensembles, the use of arbitrary linear block codes as component codes
is combined with the further design of local Tanner graph connectivity through
the use of multiple edge types. The stability condition for these code
ensembles is shown to be succinctly described in terms of the value of the
spectral radius of an appropriately defined polynomial matrix.Comment: 6 pages, 3 figures. Presented at Globecom 2011, Houston, T
Low-Density Parity-Check Codes for Nonergodic Block-Fading Channels
We solve the problem of designing powerful low-density parity-check (LDPC)
codes with iterative decoding for the block-fading channel. We first study the
case of maximum-likelihood decoding, and show that the design criterion is
rather straightforward. Unfortunately, optimal constructions for
maximum-likelihood decoding do not perform well under iterative decoding. To
overcome this limitation, we then introduce a new family of full-diversity LDPC
codes that exhibit near-outage-limit performance under iterative decoding for
all block-lengths. This family competes with multiplexed parallel turbo codes
suitable for nonergodic channels and recently reported in the literature.Comment: Submitted to the IEEE Transactions on Information Theor
Growth Rate of the Weight Distribution of Doubly-Generalized LDPC Codes: General Case and Efficient Evaluation
The growth rate of the weight distribution of irregular doubly-generalized
LDPC (D-GLDPC) codes is developed and in the process, a new efficient numerical
technique for its evaluation is presented. The solution involves simultaneous
solution of a 4 x 4 system of polynomial equations. This represents the first
efficient numerical technique for exact evaluation of the growth rate, even for
LDPC codes. The technique is applied to two example D-GLDPC code ensembles.Comment: 6 pages, 1 figure. Proc. IEEE Globecom 2009, Hawaii, USA, November 30
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