282 research outputs found
Finite Length Analysis of Irregular Repetition Slotted ALOHA in the Waterfall Region
A finite length analysis is introduced for irregular repetition slotted ALOHA
(IRSA) that enables to accurately estimate its performance in the
moderate-to-high packet loss probability regime, i.e., in the so-called
waterfall region. The analysis is tailored to the collision channel model,
which enables mapping the description of the successive interference
cancellation process onto the iterative erasure decoding of low-density
parity-check codes. The analysis provides accurate estimates of the packet loss
probability of IRSA in the waterfall region as demonstrated by Monte Carlo
simulations.Comment: Accepted for publication in the IEEE Communications Letter
Distributed Turbo-Like Codes for Multi-User Cooperative Relay Networks
In this paper, a distributed turbo-like coding scheme for wireless networks
with relays is proposed. We consider a scenario where multiple sources
communicate with a single destination with the help of a relay. The proposed
scheme can be regarded as of the decode-and-forward type. The relay decodes the
information from the sources and it properly combines and re-encodes them to
generate some extra redundancy, which is transmitted to the destination. The
amount of redundancy generated by the relay can simply be adjusted according to
requirements in terms of performance, throughput and/or power. At the
destination, decoding of the information of all sources is performed jointly
exploiting the redundancy provided by the relay in an iterative fashion. The
overall communication network can be viewed as a serially concatenated code.
The proposed distributed scheme achieves significant performance gains with
respect to the non-cooperation system, even for a very large number of users.
Furthermore, it presents a high flexibility in terms of code rate, block length
and number of users.Comment: Submitted to ICC 201
Analysis of Spatially-Coupled Counter Braids
A counter braid (CB) is a novel counter architecture introduced by Lu et al.
in 2007 for per-flow measurements on high-speed links. CBs achieve an
asymptotic compression rate (under optimal decoding) that matches the entropy
lower bound of the flow size distribution. Spatially-coupled CBs (SC-CBs) have
recently been proposed. In this work, we further analyze single-layer CBs and
SC-CBs using an equivalent bipartite graph representation of CBs. On this
equivalent representation, we show that the potential and area thresholds are
equal. We also show that the area under the extended belief propagation (BP)
extrinsic information transfer curve (defined for the equivalent graph),
computed for the expected residual CB graph when a peeling decoder equivalent
to the BP decoder stops, is equal to zero precisely at the area threshold.
This, combined with simulations and an asymptotic analysis of the Maxwell
decoder, leads to the conjecture that the area threshold is in fact equal to
the Maxwell decoding threshold and hence a lower bound on the maximum a
posteriori (MAP) decoding threshold. Finally, we present some numerical results
and give some insight into the apparent gap of the BP decoding threshold of
SC-CBs to the conjectured lower bound on the MAP decoding threshold.Comment: To appear in the IEEE Information Theory Workshop, Jeju Island,
Korea, October 201
Threshold Saturation for Nonbinary SC-LDPC Codes on the Binary Erasure Channel
We analyze the asymptotic performance of nonbinary spatially-coupled
low-density parity-check (SC-LDPC) code ensembles defined over the general
linear group on the binary erasure channel. In particular, we prove threshold
saturation of belief propagation decoding to the so called potential threshold,
using the proof technique based on potential functions introduced by Yedla
\textit{et al.}, assuming that the potential function exists. We rewrite the
density evolution of nonbinary SC-LDPC codes in an equivalent vector recursion
form which is suited for the use of the potential function. We then discuss the
existence of the potential function for the general case of vector recursions
defined by multivariate polynomials, and give a method to construct it. We
define a potential function in a slightly more general form than one by Yedla
\textit{et al.}, in order to make the technique based on potential functions
applicable to the case of nonbinary LDPC codes. We show that the potential
function exists if a solution to a carefully designed system of linear
equations exists. Furthermore, we show numerically the existence of a solution
to the system of linear equations for a large number of nonbinary LDPC code
ensembles, which allows us to define their potential function and thus prove
threshold saturation.Comment: To appear in IT Transaction
Block-Diagonal and LT Codes for Distributed Computing With Straggling Servers
We propose two coded schemes for the distributed computing problem of
multiplying a matrix by a set of vectors. The first scheme is based on
partitioning the matrix into submatrices and applying maximum distance
separable (MDS) codes to each submatrix. For this scheme, we prove that up to a
given number of partitions the communication load and the computational delay
(not including the encoding and decoding delay) are identical to those of the
scheme recently proposed by Li et al., based on a single, long MDS code.
However, due to the use of shorter MDS codes, our scheme yields a significantly
lower overall computational delay when the delay incurred by encoding and
decoding is also considered. We further propose a second coded scheme based on
Luby Transform (LT) codes under inactivation decoding. Interestingly, LT codes
may reduce the delay over the partitioned scheme at the expense of an increased
communication load. We also consider distributed computing under a deadline and
show numerically that the proposed schemes outperform other schemes in the
literature, with the LT code-based scheme yielding the best performance for the
scenarios considered.Comment: To appear in IEEE Transactions on Communication
On Frame Asynchronous Coded Slotted ALOHA: Asymptotic, Finite Length, and Delay Analysis
We consider a frame asynchronous coded slotted ALOHA (FA-CSA) system for
uncoordinated multiple access, where users join the system on a slot-by-slot
basis according to a Poisson random process and, in contrast to standard frame
synchronous CSA (FS-CSA), users are not frame-synchronized. We analyze the
performance of FA-CSA in terms of packet loss rate and delay. In particular, we
derive the (approximate) density evolution that characterizes the asymptotic
performance of FA-CSA when the frame length goes to infinity. We show that, if
the receiver can monitor the system before anyone starts transmitting, a
boundary effect similar to that of spatially-coupled codes occurs, which
greatly improves the iterative decoding threshold. Furthermore, we derive tight
approximations of the error floor (EF) for the finite frame length regime,
based on the probability of occurrence of the most frequent stopping sets. We
show that, in general, FA-CSA provides better performance in both the EF and
waterfall regions as compared to FS-CSA. Moreover, FA-CSA exhibits better delay
properties than FS-CSA.Comment: 13 pages, 12 figures. arXiv admin note: substantial text overlap with
arXiv:1604.0629
Minimum Pseudoweight Analysis of 3-Dimensional Turbo Codes
In this work, we consider pseudocodewords of (relaxed) linear programming
(LP) decoding of 3-dimensional turbo codes (3D-TCs). We present a relaxed LP
decoder for 3D-TCs, adapting the relaxed LP decoder for conventional turbo
codes proposed by Feldman in his thesis. We show that the 3D-TC polytope is
proper and -symmetric, and make a connection to finite graph covers of the
3D-TC factor graph. This connection is used to show that the support set of any
pseudocodeword is a stopping set of iterative decoding of 3D-TCs using maximum
a posteriori constituent decoders on the binary erasure channel. Furthermore,
we compute ensemble-average pseudoweight enumerators of 3D-TCs and perform a
finite-length minimum pseudoweight analysis for small cover degrees. Also, an
explicit description of the fundamental cone of the 3D-TC polytope is given.
Finally, we present an extensive numerical study of small-to-medium block
length 3D-TCs, which shows that 1) typically (i.e., in most cases) when the
minimum distance and/or the stopping distance is
high, the minimum pseudoweight (on the additive white Gaussian noise channel)
is strictly smaller than both the and the , and 2)
the minimum pseudoweight grows with the block length, at least for
small-to-medium block lengths.Comment: To appear in IEEE Transactions on Communication
Iterative Bounded Distance Decoding of Product Codes with Scaled Reliability
We propose a modified iterative bounded distance decoding of product codes.
The proposed algorithm is based on exchanging hard messages iteratively and
exploiting channel reliabilities to make hard decisions at each iteration.
Performance improvements up to 0.26 dB are achieved
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