Error-Correction Performance of Regular Ring-Linear LDPC Codes over Lee Channels
CoRR(2023)
Abstract
Most low-density parity-check (LDPC) code constructions are considered over
finite fields. In this work, we focus on regular LDPC codes over integer
residue rings and analyze their performance with respect to the Lee metric.
Their error-correction performance is studied over two channel models, in the
Lee metric. The first channel model is a discrete memoryless channel, whereas
in the second channel model an error vector is drawn uniformly at random from
all vectors of a fixed Lee weight. It is known that the two channel laws
coincide in the asymptotic regime, meaning that their marginal distributions
match. For both channel models, we derive upper bounds on the block error
probability in terms of a random coding union bound as well as sphere packing
bounds that make use of the marginal distribution of the considered channels.
We estimate the decoding error probability of regular LDPC code ensembles over
the channels using the marginal distribution and determining the expected Lee
weight distribution of a random LDPC code over a finite integer ring. By means
of density evolution and finite-length simulations, we estimate the
error-correction performance of selected LDPC code ensembles under belief
propagation decoding and a low-complexity symbol message passing decoding
algorithm and compare the performances. The analysis developed in this paper
may serve to design regular LDPC codes over integer residue rings for storage
and cryptographic application.
MoreTranslated text
Key words
Belief propagation,Lee metric,LDPC codes,ring-linear codes,symbol message passing decoding,weight enumerator
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