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The dynamical properties of finite dynamical systems (FDSs) have been investigated in the context of coding theoretic problems, such as network coding and index coding, and in the context of hat games, such as the guessing game and…
Low density parity check (LDPC) codes, initially discovered by Gallager, exhibit excellent performance in iterative decoding, approaching the Shannon limit. MDS array codes, with favorable algebraic structures, are codes suitable for…
Regular spatially-Coupled LDPC (SC-LDPC) ensembles have gained significant interest since they were shown to universally achieve the capacity of binary memoryless channels under low-complexity belief-propagation decoding. In this work, we…
Qudits offer significant advantages over qubit-based architectures, including more efficient gate compilation, reduced resource requirements, improved error-correction primitives, and enhanced capabilities for quantum communication and…
We give a construction of Quantum Low-Density Parity Check (QLDPC) codes with near-optimal rate-distance tradeoff and efficient list decoding up to the Johnson bound in polynomial time. Previous constructions of list decodable good distance…
This paper is concerned with linear superposition systems in which all components of the superimposed signal are coded with an identical binary low-density parity-check (LDPC) code.
It is proved in this work that exhaustively determining bad patterns in arbitrary, finite low-density parity-check (LDPC) codes, including stopping sets for binary erasure channels (BECs) and trapping sets (also known as near-codewords) for…
We study the performance of nonbinary low-density parity-check (LDPC) codes over finite integer rings over two channels that arise from the Lee metric. The first channel is a discrete memory-less channel (DMC) matched to the Lee metric. The…
We provide a comprehensive view of various phase transitions in random $K$-satisfiability problems solved by stochastic-local-search algorithms. In particular, we focus on the finite-size scaling (FSS) exponent, which is mathematically…
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…
Fair-density parity-check (FDPC) codes have been recently introduced demonstrating improved performance compared to low-density parity-check (LDPC) codes standardized in 5G systems particularly in high-rate regimes. In this paper, we…
To obtain a better cycle-structure is still a challenge for the low-density parity-check (LDPC) code design. This paper formulates two metrics firstly so that the progressive edge-growth (PEG) algorithm and the approximate cycle extrinsic…
We introduce Decision Tree Decoders (DTDs), which rely only on the sparsity of the binary check matrix, making them broadly applicable for decoding any quantum low-density parity-check (qLDPC) code and fault-tolerant quantum circuits. DTDs…
The complexity-performance trade-off is a fundamental aspect of the design of low-density parity-check (LDPC) codes. In this paper, we consider LDPC codes for the binary erasure channel (BEC), use code rate for performance metric, and…
The distance-3 cyclic lowest-density MDS array code (called the C-Code) is a good candidate for RAID 6 because of its optimal storage efficiency, optimal update complexity, optimal length, and cyclic symmetry. In this paper, the underlying…
Quantum low-density parity-check (QLDPC) codes have been proven to achieve higher minimum distances at higher code rates than surface codes. However, this family of codes imposes stringent latency requirements and poor performance under…
One of the phenomena that influences significantly the performance of low-density parity-check codes is known as trapping sets. An $(a,b)$ elementary trapping set, or simply an ETS where $a$ is the size and $b$ is the number of degree-one…
We analyze the finite-length performance of spatially coupled low-density parity-check (SC-LDPC) codes under window decoding over the binary erasure channel. In particular, we propose a refinement of the scaling law by Olmos and Urbanke for…
A Lattice is a partially ordered set where both least upper bound and greatest lower bound of any pair of elements are unique and exist within the set. K\"{o}tter and Kschischang proved that codes in the linear lattice can be used for error…
We propose a new type of short to moderate block-length, linear error-correcting codes, called moderate-density parity-check (MDPC) codes. The number of ones of the parity-check matrix of the codes presented is typically higher than the…