5,198 research outputs found
Finite-Length Scaling and Finite-Length Shift for Low-Density Parity-Check Codes
Consider communication over the binary erasure channel BEC using random
low-density parity-check codes with finite-blocklength n from `standard'
ensembles. We show that large error events is conveniently described within a
scaling theory, and explain how to estimate heuristically their effect. Among
other quantities, we consider the finite length threshold e(n), defined by
requiring a block error probability P_B = 1/2. For ensembles with minimum
variable degree larger than two, the following expression is argued to hold
e(n) = e -e_1 n^{-2/3} +\Theta(n^{-1}) with a calculable shift} parameter
e_1>0.Comment: 42nd Allerton Conference on Communication, Control and Computing
(invited paper
Finite-Length Scaling for Iteratively Decoded LDPC Ensembles
In this paper we investigate the behavior of iteratively decoded low-density
parity-check codes over the binary erasure channel in the so-called ``waterfall
region." We show that the performance curves in this region follow a very basic
scaling law. We conjecture that essentially the same scaling behavior applies
in a much more general setting and we provide some empirical evidence to
support this conjecture. The scaling law, together with the error floor
expressions developed previously, can be used for fast finite-length
optimization.Comment: 45 pages, 14 figure
Analyzing Finite-length Protograph-based Spatially Coupled LDPC Codes
The peeling decoding for spatially coupled low-density parity-check (SC-LDPC)
codes is analyzed for a binary erasure channel. An analytical calculation of
the mean evolution of degree-one check nodes of protograph-based SC-LDPC codes
is given and an estimate for the covariance evolution of degree-one check nodes
is proposed in the stable decoding phase where the decoding wave propagates
along the chain of coupled codes. Both results are verified numerically.
Protograph-based SC-LDPC codes turn out to have a more robust behavior than
unstructured random SC-LDPC codes. Using the analytically calculated
parameters, the finite- length scaling laws for these constructions are given
and verified by numerical simulations.Comment: 5 pages, 6 figures, submitted to ISIT 201
Improving the Finite-Length Performance of Spatially Coupled LDPC Codes by Connecting Multiple Code Chains
In this paper, we analyze the finite-length performance of codes on graphs
constructed by connecting spatially coupled low-density parity-check (SC-LDPC)
code chains. Successive (peeling) decoding is considered for the binary erasure
channel (BEC). The evolution of the undecoded portion of the bipartite graph
remaining after each iteration is analyzed as a dynamical system. When
connecting short SC-LDPC chains, we show that, in addition to superior
iterative decoding thresholds, connected chain ensembles have better
finite-length performance than single chain ensembles of the same rate and
length. In addition, we present a novel encoding/transmission scheme to improve
the performance of a system using long SC-LDPC chains, where, instead of
transmitting codewords corresponding to a single SC-LDPC chain independently,
we connect consecutive chains in a multi-layer format to form a connected chain
ensemble. We refer to such a transmission scheme to as continuous chain (CC)
transmission of SC-LDPC codes. We show that CC transmission can be implemented
with no significant increase in encoding/decoding complexity or decoding delay
with respect a system using a single SC-LDPC code chain for encoding.Comment: Submitted to IEEE Transactions on Information Theory, February 201
Continuous Transmission of Spatially-Coupled LDPC Code Chains
We propose a novel encoding/transmission scheme called continuous chain (CC)
transmission that is able to improve the finite-length performance of a system
using spatially-coupled low-density parity-check (SC-LDPC) codes. In CC
transmission, instead of transmitting a sequence of independent codewords from
a terminated SC-LDPC code chain, we connect multiple chains in a layered
format, where encoding, transmission, and decoding are now performed in a
continuous fashion. The connections between chains are created at specific
points, chosen to improve the finite-length performance of the code structure
under iterative decoding. We describe the design of CC schemes for different
SC-LDPC code ensembles constructed from protographs: a (J,K)-regular SC-LDPC
code chain, a spatially-coupled repeat-accumulate (SC-RA) code, and a
spatially-coupled accumulate-repeat-jagged-accumulate (SC- ARJA) code. In all
cases, significant performance improvements are reported and, in addition, it
is shown that using CC transmission only requires a small increase in decoding
complexity and decoding delay with respect to a system employing a single
SC-LDPC code chain for transmission.Comment: arXiv admin note: text overlap with arXiv:1402.717
Hybrid Decoding of Finite Geometry LDPC Codes
For finite geometry low-density parity-check codes, heavy row and column
weights in their parity check matrix make the decoding with even Min-Sum (MS)
variants computationally expensive. To alleviate it, we present a class of
hybrid schemes by concatenating a parallel bit flipping (BF) variant with an
Min-Sum (MS) variant. In most SNR region of interest, without compromising
performance or convergence rate, simulation results show that the proposed
hybrid schemes can save substantial computational complexity with respect to MS
variant decoding alone. Specifically, the BF variant, with much less
computational complexity, bears most decoding load before resorting to MS
variant. Computational and hardware complexity is also elaborated to justify
the feasibility of the hybrid schemes.Comment: 19 pages, 5 figures, 5 table
Bandwidth Efficient and Rate-Matched Low-Density Parity-Check Coded Modulation
A new coded modulation scheme is proposed. At the transmitter, the
concatenation of a distribution matcher and a systematic binary encoder
performs probabilistic signal shaping and channel coding. At the receiver, the
output of a bitwise demapper is fed to a binary decoder. No iterative demapping
is performed. Rate adaption is achieved by adjusting the input distribution and
the transmission power. The scheme is applied to bipolar amplitude shift keying
(ASK) constellations with equidistant signal points and it is directly
applicable to two-dimensional quadrature amplitude modulation (QAM). The scheme
is implemented by using the DVB-S2 low-density parity-check (LDPC) codes. At a
frame error rate of 1e-3, the new scheme operates within less than 1 dB of the
AWGN capacity 0.5log2(1+SNR) at any spectral efficiency between 1 and 5
bits/s/Hz by using only 5 modes, i.e., 4-ASK with code rate 2/3, 8-ASK with
3/4, 16-ASK and 32-ASK with 5/6 and 64-ASK with 9/10.Comment: 13 pages, 11 figures, 10 table
Optimization of Bit Mapping and Quantized Decoding for Off-the-Shelf Protograph LDPC Codes with Application to IEEE 802.3ca
Protograph-based, off-the-shelf low-density parity-check (LDPC) codes are
optimized for higher-order modulation and quantized sum-product decoders. As an
example, for the recently proposed LDPC code from the upcoming IEEE 802.3ca
standard for passive optical networks (PONs), an optimized mapping of the bit
channels originating from bit-metric decoding to the protograph variable nodes
gains 0.4 dB and 0.3 dB at a bit-error rate of 1e-6 for shaped and uniform
signaling, respectively. Furthermore, the clipping value for a quantized
sum-product LDPC decoder is optimized via discretized density evolution.Comment: Invited paper for ISTC 2018, Session "Ultra-High Throughput Coding
for Fibre-Optical and B5G Wireless Communications
Optimized IR-HARQ Schemes Based on Punctured LDPC Codes over the BEC
We study incremental redundancy hybrid ARQ (IR-HARQ) schemes based on
punctured, finite-length, LDPC codes. The transmission is assumed to take place
over time varying binary erasure channels, such as mobile wireless channels at
the applications layer. We analyze and optimize the throughput and delay
performance of these IR-HARQ protocols under iterative, message-passing
decoding. We derive bounds on the performance that are achievable by such
schemes, and show that, with a simple extension, the iteratively decoded,
punctured LDPC code based IR-HARQ protocol can be made rateless, and operating
close to the general theoretical optimum for a wide range of channel erasure
rates.Comment: IEEE Transactions on Information Theor
Quantum "hyperbicycle" low-density parity check codes with finite rate
We introduce a "hyperbicycle" ansatz for quantum codes which gives the
hypergraph-product (generalized toric) codes by Tillich and Z\'emor and
generalized bicycle codes by MacKay et al. as limiting cases. The construction
allows for both the lower and the upper bounds on the minimum distance; they
scale as a square root of the block length. Many of thus defined codes have
finite rate and a limited-weight stabilizer generators, an analog of classical
low-density parity check (LDPC) codes. Compared to the hypergraph-product
codes, hyperbicycle codes generally have wider range of parameters; in
particular, they can have higher rate while preserving the (estimated) error
threshold.Comment: 13 pages, 4 figure
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