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We derive bounds on the asymptotic density of parity-check matrices and the achievable rates of binary linear block codes transmitted over memoryless binary-input output-symmetric (MBIOS) channels. The lower bounds on the density of…
Quantum low-density parity-check codes are promising candidates for quantum error correcting codes as they might offer more resource-efficient alternatives to surface code architectures. In particular, bivariate bicycle codes have recently…
Although real-coded differential evolution (DE) algorithms can perform well on continuous optimization problems (CoOPs), it is still a challenging task to design an efficient binary-coded DE algorithm. Inspired by the learning mechanism of…
Recently, we introduced a new class of finite alphabet iterative decoders (FAIDs) for low-density parity-check (LDPC) codes. These decoders are capable of surpassing belief propagation in the error floor region on the Binary Symmetric…
This paper considers the optimization of multi-edge type low-density parity-check (METLDPC) codes to maximize the decoding threshold. We propose an algorithm to jointly optimize the node degree distribution and the multi-edge structure of…
In this paper, we shed light on how an adaptive, efficient error coding in the transport layer helps ensure the application requirements. We recap the use of MDS codes and show that binary coding can significantly reduce the complexity and…
We study the secure decentralized Pliable Index CODing (PICOD) problem with circular side information sets at the users. The security constraint forbids every user to decode more than one message while a decentralized setting means there is…
The explosion of the amount of data stored in cloud systems calls for more efficient paradigms for redundancy. While replication is widely used to ensure data availability, erasure correcting codes provide a much better trade-off between…
Finite alphabet iterative decoders (FAIDs) for LDPC codes were recently shown to be capable of surpassing the Belief Propagation (BP) decoder in the error floor region on the Binary Symmetric channel (BSC). More recently, the technique of…
The design of binary error-correcting codes is a challenging optimization problem with several applications in telecommunications and storage, which has also been addressed with metaheuristic techniques and evolutionary algorithms. Still,…
Iterative decoding is essential in modern communication systems, especially optical communications, where error-correcting codes such as turbo product codes (TPC) and staircase codes are widely employed. A key factor in achieving high error…
We consider locally repairable codes over small fields and propose constructions of optimal cyclic and linear codes in terms of the dimension for a given distance and length. Four new constructions of optimal linear codes over small fields…
In this paper, code decompositions (a.k.a. code nestings) are used to design binary polarization kernels. The proposed kernels are in general non-linear. They provide a better polarization exponent than the previously known kernels of the…
Tailored topological stabilizer codes in two dimensions have been shown to exhibit high storage threshold error rates and improved subthreshold performance under biased Pauli noise. Three-dimensional (3D) topological codes can allow for…
A new approach for combining non-binary low-density parity-check (NB-LDPC) codes with higher-order modulation and probabilistic amplitude shaping (PAS) is presented. Instead of symbol-metric decoding (SMD), a bit-metric decoder (BMD) is…
Error correction codes are a crucial part of the physical communication layer, ensuring the reliable transfer of data over noisy channels. The design of optimal linear block codes capable of being efficiently decoded is of major concern,…
We propose several improvements for Linear Programming (LP) decoding algorithms for High Density Parity Check (HDPC) codes. First, we use the automorphism groups of a code to create parity check matrix diversity and to generate valid cuts…
In this paper, we design the optimal rate capacity approaching irregular Low-Density Parity-Check code ensemble over Binary Erasure Channel, by using practical Semi-Definite Programming approach. Our method does not use any relaxation or…
Polar codes are a family of capacity-achieving codes that have explicit and low-complexity construction, encoding, and decoding algorithms. Decoding of polar codes is based on the successive-cancellation decoder, which decodes in a bit-…
Inner and outer bounds are derived on the optimal performance of fixed length block codes on discrete memoryless channels with feedback and errors-and-erasures decoding. First an inner bound is derived using a two phase encoding scheme with…