951 research outputs found
Systematic Transmission With Fountain Parity Checks for Erasure Channels With Stop Feedback
In this paper, we present new achievability bounds on the maximal achievable
rate of variable-length stop-feedback (VLSF) codes operating over a binary
erasure channel (BEC) at a fixed message size . We provide new bounds
for VLSF codes with zero error, infinite decoding times and with nonzero error,
finite decoding times. Both new achievability bounds are proved by constructing
a new VLSF code that employs systematic transmission of the first bits
followed by random linear fountain parity bits decoded with a rank decoder. For
VLSF codes with infinite decoding times, our new bound outperforms the
state-of-the-art result for BEC by Devassy \emph{et al.} in 2016. We also give
a negative answer to the open question Devassy \emph{et al.} put forward on
whether the backoff to capacity at is fundamental. For VLSF
codes with finite decoding times, numerical evaluations show that the
achievable rate for VLSF codes with a moderate number of decoding times closely
approaches that for VLSF codes with infinite decoding times.Comment: 7 pages, double column, 4 figures; comments are welcome! changes in
v2: corrected 2 typos in v1. arXiv admin note: substantial text overlap with
arXiv:2205.1539
Joint source-channel coding with feedback
This paper quantifies the fundamental limits of variable-length transmission
of a general (possibly analog) source over a memoryless channel with noiseless
feedback, under a distortion constraint. We consider excess distortion, average
distortion and guaranteed distortion (-semifaithful codes). In contrast to
the asymptotic fundamental limit, a general conclusion is that allowing
variable-length codes and feedback leads to a sizable improvement in the
fundamental delay-distortion tradeoff. In addition, we investigate the minimum
energy required to reproduce source samples with a given fidelity after
transmission over a memoryless Gaussian channel, and we show that the required
minimum energy is reduced with feedback and an average (rather than maximal)
power constraint.Comment: To appear in IEEE Transactions on Information Theor
Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications
Coding; Communications; Engineering; Networks; Information Theory; Algorithm
On generalized LDPC codes for ultra reliable communication
Ultra reliable low latency communication (URLLC) is an important feature in
future mobile communication systems, as they will require high data rates, large
system capacity and massive device connectivity [11]. To meet such stringent
requirements, many error-correction codes (ECC)s are being investigated; turbo
codes, low density parity check (LDPC) codes, polar codes and convolutional codes
[70, 92, 38], among many others. In this work, we present generalized low density
parity check (GLDPC) codes as a promising candidate for URLLC.
Our proposal is based on a novel class of GLDPC code ensembles, for which
new analysis tools are proposed. We analyze the trade-o_ between coding rate and
asymptotic performance of a class of GLDPC codes constructed by including a
certain fraction of generalized constraint (GC) nodes in the graph. To incorporate
both bounded distance (BD) and maximum likelihood (ML) decoding at GC nodes
into our analysis without resorting to multi-edge type of degree distribution (DD)s,
we propose the probabilistic peeling decoding (P-PD) algorithm, which models the
decoding step at every GC node as an instance of a Bernoulli random variable with
a successful decoding probability that depends on both the GC block code as well
as its decoding algorithm. The P-PD asymptotic performance over the BEC can
be efficiently predicted using standard techniques for LDPC codes such as Density
evolution (DE) or the differential equation method. We demonstrate that the
simulated P-PD performance accurately predicts the actual performance of the
GLPDC code under ML decoding at GC nodes. We illustrate our analysis for
GLDPC code ensembles with regular and irregular DDs.
This design methodology is applied to construct practical codes for URLLC.
To this end, we incorporate to our analysis the use of quasi-cyclic (QC) structures,
to mitigate the code error floor and facilitate the code very large scale integration
(VLSI) implementation. Furthermore, for the additive white Gaussian noise
(AWGN) channel, we analyze the complexity and performance of the message
passing decoder with various update rules (including standard full-precision sum product and min-sum algorithms) and quantization schemes. The block error rate
(BLER) performance of the proposed GLDPC codes, combined with a complementary
outer code, is shown to outperform a variety of state-of-the-art codes, for
URLLC, including LDPC codes, polar codes, turbo codes and convolutional codes,
at similar complexity rates.Programa Oficial de Doctorado en Multimedia y ComunicacionesPresidente: Juan José Murillo Fuentes.- Secretario: Matilde Pilar Sánchez Fernández.- Vocal: Javier Valls Coquilla
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