3,346 research outputs found
Spatially Coupled LDPC Codes Constructed from Protographs
In this paper, we construct protograph-based spatially coupled low-density
parity-check (SC-LDPC) codes by coupling together a series of L disjoint, or
uncoupled, LDPC code Tanner graphs into a single coupled chain. By varying L,
we obtain a flexible family of code ensembles with varying rates and frame
lengths that can share the same encoding and decoding architecture for
arbitrary L. We demonstrate that the resulting codes combine the best features
of optimized irregular and regular codes in one design: capacity approaching
iterative belief propagation (BP) decoding thresholds and linear growth of
minimum distance with block length. In particular, we show that, for
sufficiently large L, the BP thresholds on both the binary erasure channel
(BEC) and the binary-input additive white Gaussian noise channel (AWGNC)
saturate to a particular value significantly better than the BP decoding
threshold and numerically indistinguishable from the optimal maximum
a-posteriori (MAP) decoding threshold of the uncoupled LDPC code. When all
variable nodes in the coupled chain have degree greater than two,
asymptotically the error probability converges at least doubly exponentially
with decoding iterations and we obtain sequences of asymptotically good LDPC
codes with fast convergence rates and BP thresholds close to the Shannon limit.
Further, the gap to capacity decreases as the density of the graph increases,
opening up a new way to construct capacity achieving codes on memoryless
binary-input symmetric-output (MBS) channels with low-complexity BP decoding.Comment: Submitted to the IEEE Transactions on Information Theor
Bilayer Low-Density Parity-Check Codes for Decode-and-Forward in Relay Channels
This paper describes an efficient implementation of binning for the relay
channel using low-density parity-check (LDPC) codes. We devise bilayer LDPC
codes to approach the theoretically promised rate of the decode-and-forward
relaying strategy by incorporating relay-generated information bits in
specially designed bilayer graphical code structures. While conventional LDPC
codes are sensitively tuned to operate efficiently at a certain channel
parameter, the proposed bilayer LDPC codes are capable of working at two
different channel parameters and two different rates: that at the relay and at
the destination. To analyze the performance of bilayer LDPC codes, bilayer
density evolution is devised as an extension of the standard density evolution
algorithm. Based on bilayer density evolution, a design methodology is
developed for the bilayer codes in which the degree distribution is iteratively
improved using linear programming. Further, in order to approach the
theoretical decode-and-forward rate for a wide range of channel parameters,
this paper proposes two different forms bilayer codes, the bilayer-expurgated
and bilayer-lengthened codes. It is demonstrated that a properly designed
bilayer LDPC code can achieve an asymptotic infinite-length threshold within
0.24 dB gap to the Shannon limits of two different channels simultaneously for
a wide range of channel parameters. By practical code construction,
finite-length bilayer codes are shown to be able to approach within a 0.6 dB
gap to the theoretical decode-and-forward rate of the relay channel at a block
length of and a bit-error probability (BER) of . Finally, it is
demonstrated that a generalized version of the proposed bilayer code
construction is applicable to relay networks with multiple relays.Comment: Submitted to IEEE Trans. Info. Theor
Irregular Turbo Codes in Block-Fading Channels
We study irregular binary turbo codes over non-ergodic block-fading channels.
We first propose an extension of channel multiplexers initially designed for
regular turbo codes. We then show that, using these multiplexers, irregular
turbo codes that exhibit a small decoding threshold over the ergodic
Gaussian-noise channel perform very close to the outage probability on
block-fading channels, from both density evolution and finite-length
perspectives.Comment: to be presented at the IEEE International Symposium on Information
Theory, 201
Bilayer Protograph Codes for Half-Duplex Relay Channels
Despite encouraging advances in the design of relay codes, several important
challenges remain. Many of the existing LDPC relay codes are tightly optimized
for fixed channel conditions and not easily adapted without extensive
re-optimization of the code. Some have high encoding complexity and some need
long block lengths to approach capacity. This paper presents a high-performance
protograph-based LDPC coding scheme for the half-duplex relay channel that
addresses simultaneously several important issues: structured coding that
permits easy design, low encoding complexity, embedded structure for convenient
adaptation to various channel conditions, and performance close to capacity
with a reasonable block length. The application of the coding structure to
multi-relay networks is demonstrated. Finally, a simple new methodology for
evaluating the end-to-end error performance of relay coding systems is
developed and used to highlight the performance of the proposed codes.Comment: Accepted in IEEE Trans. Wireless Com
A Fast Convergence Density Evolution Algorithm for Optimal Rate LDPC Codes in BEC
We derive a new fast convergent Density Evolution algorithm for finding
optimal rate Low-Density Parity-Check (LDPC) codes used over the binary erasure
channel (BEC). The fast convergence property comes from the modified Density
Evolution (DE), a numerical method for analyzing the behavior of iterative
decoding convergence of a LDPC code. We have used the method of [16] for
designing of a LDPC code with optimal rate. This has been done for a given
parity check node degree distribution, erasure probability and specified DE
constraint. The fast behavior of DE and found optimal rate with this method
compare with the previous DE constraint.Comment: This Paper is a draft of final paper which represented in 7th
International Symposium on Telecommunications (IST'2014
On Universal Properties of Capacity-Approaching LDPC Ensembles
This paper is focused on the derivation of some universal properties of
capacity-approaching low-density parity-check (LDPC) code ensembles whose
transmission takes place over memoryless binary-input output-symmetric (MBIOS)
channels. Properties of the degree distributions, graphical complexity and the
number of fundamental cycles in the bipartite graphs are considered via the
derivation of information-theoretic bounds. These bounds are expressed in terms
of the target block/ bit error probability and the gap (in rate) to capacity.
Most of the bounds are general for any decoding algorithm, and some others are
proved under belief propagation (BP) decoding. Proving these bounds under a
certain decoding algorithm, validates them automatically also under any
sub-optimal decoding algorithm. A proper modification of these bounds makes
them universal for the set of all MBIOS channels which exhibit a given
capacity. Bounds on the degree distributions and graphical complexity apply to
finite-length LDPC codes and to the asymptotic case of an infinite block
length. The bounds are compared with capacity-approaching LDPC code ensembles
under BP decoding, and they are shown to be informative and are easy to
calculate. Finally, some interesting open problems are considered.Comment: Published in the IEEE Trans. on Information Theory, vol. 55, no. 7,
pp. 2956 - 2990, July 200
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
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