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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…
Each classical public-coin protocol for coin flipping is naturally associated with a quantum protocol for weak coin flipping. The quantum protocol is obtained by replacing classical randomness with quantum entanglement and by adding a cheat…
To strengthen the anonymity of Bitcoin, several centralized coin-mixing providers (mixers) such as BitcoinFog.com, BitLaundry.com, and Blockchain.info assist users to mix Bitcoins through CoinJoin transactions with multiple inputs and…
This paper investigates fundamental properties of nonlinear binary codes by looking at the codebook matrix not row-wise (codewords), but column-wise. The family of weak flip codes is presented and shown to contain many beautiful properties.…
While cycling offers an attractive option for sustainable transportation, many potential cyclists are discouraged from taking up cycling due to the lack of suitable and safe infrastructure. Efficiently mapping cycling infrastructure across…
We study the parameterized complexity of a recently introduced multi-agent variant of the Kidney Exchange problem. Given a directed graph $G$ and integers $d$ and $k$, the standard problem asks whether $G$ contains a packing of…
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)…
The original dense coding protocol is achieved via quantum channel generated between a single Cooper pair and a cavity. The dynamics of the coded and decoded information are investigated for different values of the channel's parameters. The…
This paper is devoted to the finite-length analysis of turbo decoding over the binary erasure channel (BEC). The performance of iterative belief-propagation (BP) decoding of low-density parity-check (LDPC) codes over the BEC can be…
Although quantum key distribution (QKD) comes from the development of quantum theory, the implementation of a practical QKD system does involve a lot of classical process, such as key reconciliation and privacy amplification, which is…
We present an analytical theory of greedy peeling decoding for bivariate bicycle (BB) codes under circuit-level noise. The deferred greedy decoder achieves 330x latency reduction over belief propagation (BP) at p = 10^{-3} while maintaining…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, a class of three-weight…
The performance of iterative decoding techniques for linear block codes correcting erasures depends very much on the sizes of the stopping sets associated with the underlying Tanner graph, or, equivalently, the parity-check matrix…
Cyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer applications due to their efficient encoding and decoding algorithms. In…
The encoding complexity of a general (en,ek) quasi-cyclic code is O[(e^2)(n-k)k]. This paper presents a novel low-complexity encoding algorithm for quasi-cyclic (QC) codes based on matrix transformation. First, a message vector is encoded…
Quantum low-density parity-check (QLDPC) codes have emerged as a promising technique for quantum error correction. A variety of decoders have been proposed for QLDPC codes and many of them utilize belief propagation (BP) decoding in some…
The relation between parity-check matrices of quasi-cyclic (QC) low-density parity-check (LDPC) codes and biadjacency matrices of bipartite graphs supports searching for powerful LDPC block codes. Using the principle of tailbiting, compact…
In this paper, we propose a new variant of the McEliece cryptosystem using two families of quasi-cyclic codes: low density parity check codes (QC-LDPC) and moderate density parity check codes (QC-MDPC). Due to the low weight codewords in…
Block-encoding is a critical subroutine in quantum computing, enabling the transformation of classical data into a matrix representation within a quantum circuit. The resource trade-offs in simulating a block-encoding can be quantified by…
In the literature, strong coin tossing protocols based on bit commitment have been proposed. Here we examine a protocol that instead tries to achieve the task by sharing entanglement securely. The protocol uses only qubits, and has bias…