29 research outputs found
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
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
New Codes on Graphs Constructed by Connecting Spatially Coupled Chains
A novel code construction based on spatially coupled low-density parity-check
(SC-LDPC) codes is presented. The proposed code ensembles are described by
protographs, comprised of several protograph-based chains characterizing
individual SC-LDPC codes. We demonstrate that code ensembles obtained by
connecting appropriately chosen SC-LDPC code chains at specific points have
improved iterative decoding thresholds compared to those of single SC-LDPC
coupled chains. In addition, it is shown that the improved decoding properties
of the connected ensembles result in reduced decoding complexity required to
achieve a specific bit error probability. The constructed ensembles are also
asymptotically good, in the sense that the minimum distance grows linearly with
the block length. Finally, we show that the improved asymptotic properties of
the connected chain ensembles also translate into improved finite length
performance.Comment: Submitted to IEEE Transactions on Information Theor
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
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 Nearly-Regular LDPC Code Ensembles for Rate-Flexible Code Design
Spatially coupled regular LDPC code ensembles have outstanding performance with belief propagation decoding and can perform close to the Shannon limit. In this paper we investigate the suitability of coupled regular LDPC code ensembles with respect to rate-flexibility. Regular ensembles with good performance and low complexity exist for a variety of specific code rates. On the other hand it can be observed that outside this set of favorable rational rates the complexity and performance become unreasonably high. We therefore propose ensembles with slight irregularity that allow us to smoothly cover the complete range of rational rates. Our simple construction allows a performance with negligible gap to the Shannon limit while maintaining complexity as low as for the best regular code ensembles. At the same time the construction guarantees that asymptotically the minimum distance grows linearly with the length of the coupled blocks
Low-Density Graph Codes for slow fading Relay Channels
We study Low-Density Parity-Check (LDPC) codes with iterative decoding on
block-fading (BF) Relay Channels. We consider two users that employ coded
cooperation, a variant of decode-and-forward with a smaller outage probability
than the latter. An outage probability analysis for discrete constellations
shows that full diversity can be achieved only when the coding rate does not
exceed a maximum value that depends on the level of cooperation. We derive a
new code structure by extending the previously published full-diversity
root-LDPC code, designed for the BF point-to-point channel, to exhibit a
rate-compatibility property which is necessary for coded cooperation. We
estimate the asymptotic performance through a new density evolution analysis
and the word error rate performance is determined for finite length codes. We
show that our code construction exhibits near-outage limit performance for all
block lengths and for a range of coding rates up to 0.5, which is the highest
possible coding rate for two cooperating users.Comment: Accepted for publication in IEEE Transactions on Information Theor