Publication: On generalized LDPC codes for ultra reliable communication
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2019-01-31
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2019-01-31
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Abstract
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.
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Keywords
Ultra Reliable Low Latency Communication (URLLC), Low Density Parity Check (LDPC), Generalized Low Density Parity Check (GLDPC)