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Low-density parity-check (LDPC) codes are among the most prominent error-correction schemes. They find application to fortify various modern storage, communication, and computing systems. Protograph-based (PB) LDPC codes offer many degrees…
This paper investigates the design of low-complexity error correction codes for the verification step in continuous variable quantum key distribution (CVQKD) systems. We design new coding schemes based on quasi-cyclic repeat-accumulate…
Quantum error correction is an indispensable ingredient for scalable quantum computing. In this Perspective we discuss a particular class of quantum codes called low-density parity-check (LDPC) quantum codes. The codes we discuss are…
We consider generalized low-density parity-check (GLDPC) codes with component codes that are duals of Cordaro-Wagner codes. Two efficient decoding algorithms are proposed: one based on Hartmann-Rudolph processing, analogous to Sum-Product…
LDPC lattices were the first family of lattices that equipped with iterative decoding algorithms under which they perform very well in high dimensions. In this paper, we introduce quasi cyclic low density parity check (QC-LDPC) lattices as…
Polar codes are novel and efficient error correcting codes with low encoding and decoding complexities. These codes have a channel dependent generator matrix which is determined by the code dimension, code length and transmission channel…
Density evolution (DE) is one of the most powerful analytical tools for low-density parity-check (LDPC) codes on memoryless binary-input/symmetric-output channels. The case of non-symmetric channels is tackled either by the LDPC coset code…
In this paper, we propose new coupled codes constructed by overlapping circular spatially-coupled low-density parity-check (SC-LDPC) codes, which show better asymptotic and finite-length decoding performance compared to the conventional…
Post-quantum cryptography has gained attention due to the need for secure cryptographic systems in the face of quantum computing. Code-based and lattice-based cryptography are two prominent approaches, both heavily studied within the NIST…
In this Phd thesis discusses modern methods for constructing MET QC-LDPC codes with a given error correction ("waterfall, error-floor") and complexity (parallelism level according circulant size plus scheduler orthogonality of checks)…
Building scalable quantum computers requires quantum error-correcting codes that enable reliable operations in the presence of noise. Motivated by such need, this paper introduces two constructions of high-rate, quantum dual-containing (DC)…
Quasi-cyclic (QC) low-density parity-check (LDPC) codes are a class of LDPC codes with a simple construction facilitating hardware implementation while achieving excellent performance. In this paper, we introduce an algorithm that…
Code-based public-key cryptosystems based on QC-LDPC and QC-MDPC codes are promising post-quantum candidates to replace quantum vulnerable classical alternatives. However, a new type of attacks based on Bob's reactions have recently been…
A protograph-based low-density parity-check (LDPC) code design technique for bandwidth-efficient coded modulation is presented. The approach jointly optimizes the LDPC code node degrees and the mapping of the coded bits to the…
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…
This paper proposes a "quasi-synchronous" design approach for signal processing circuits, in which timing violations are permitted, but without the need for a hardware compensation mechanism. The case of a low-density parity-check (LDPC)…
Recently, Branco da Silva and Silva described an efficient encoding and decoding algorithm for Construction D$^\prime$ lattices. Using their algorithm, we propose a Construction D$^\prime$ lattice based on binary quasi-cyclic low-density…
As massive graphs become more prevalent, there is a rapidly growing need for scalable algorithms that solve classical graph problems, such as maximum matching and minimum vertex cover, on large datasets. For massive inputs, several…
Due to their weak algebraic structure, low rank parity check (LRPC) codes have been employed in several post-quantum cryptographic schemes. In this paper we propose new improved decoding algorithms for (n, k) LRPC codes of dual rank weight…
We propose a low-complexity method to find quasi-cyclic low-density parity-check block codes with girth 10 or 12 and shorter length than those designed through classical approaches. The method is extended to time-invariant spatially coupled…