Related papers: Weight distribution bounds to relate minimum dista…
Polar codes are usually constructed by ranking synthetic bit-channels according to reliability, which guarantees capacity-achieving behavior but can yield poor low-weight spectra at short and moderate lengths. Recent algebraic results…
flip is an extremely simple and maximally local classical decoder which has been used to great effect in certain classes of classical codes. When applied to quantum codes there exist constant-weight errors (such as half of a stabiliser)…
We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding…
We investigate random spatially coupled low-density parity-check (SC-LDPC) code ensembles over finite fields. Under different variable-node edge-spreading rules, the random Tanner graphs of several coupled ensembles are defined by multiple…
The performance of algebraic soft-decision decoding of Reed-Solomon codes using bit-level soft information is investigated. Optimal multiplicity assignment strategies of algebraic soft-decision decoding with infinite cost are first studied…
This paper considers error probabilities of random codes for memoryless channels in the fixed-rate regime. Random coding is a fundamental scheme to achieve the channel capacity and many studies have been conducted for the asymptotics of the…
Quantum error correction is capable of digitizing quantum noise and increasing the robustness of qubits. Typically, error correction is designed with the target of eliminating all errors - making an error so unlikely it can be assumed that…
In this work it is shown that locally repairable codes (LRCs) can be list-decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing the local error-correction capabilities. The corresponding decoding radius…
We recently showed in [1] the superiority of certain structured coding matrices ensembles (such as partial row-orthogonal) for sparse superposition codes when compared with purely random matrices with i.i.d. entries, both…
A crucial insight for practical quantum error correction is that different types of errors, such as single-qubit Pauli operators, typically occur with different probabilities. Finding an optimal quantum code under such biased noise is a…
Motivated by applications to distributed storage, Gopalan \textit{et al} recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a parity-check…
Polar codes were introduced in 2009 and proven to achieve the symmetric capacity of any binary-input discrete memoryless channel under low-complexity successive cancellation decoding. In this thesis, we construct cyclic polar codes based on…
In the practical network communications, many internal nodes in the network are required to not only transmit messages but decode source messages. For different applications, four important classes of linear network codes in network coding…
Quantum error correction (QEC) is often implemented on hardware that experiences biased noise, where dephasing errors occur more frequently than other errors. This has motivated many recent efforts to develop bias-tailored QEC codes, such…
Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…
Error probabilities of random codes for memoryless channels are considered in this paper. In the area of communication systems, admissible error probability is very small and it is sometimes more important to discuss the relative gap…
Density evolution is one of the most powerful analytical tools for low-density parity-check (LDPC) codes and graph codes with message passing decoding algorithms. With channel symmetry as one of its fundamental assumptions, density…
Consider the transmission of a polar code of block length $N$ and rate $R$ over a binary memoryless symmetric channel $W$ and let $P_e$ be the block error probability under successive cancellation decoding. In this paper, we develop new…
This paper focuses on finite-dimensional upper and lower bounds on decodable thresholds of Zm and binary low-density parity-check (LDPC) codes, assuming belief propagation decoding on memoryless channels. A concrete framework is presented,…
Cyclic codes are an important class of linear codes. Bounding the minimum distance of cyclic codes is a long-standing research topic in coding theory, and several well-known and basic results have been developed on this topic. Recently,…