Related papers: A Combinatorial Approach to Avoiding Weak Keys in …
We propose a scalable decoding framework for correcting correlated hook errors in stabilizer measurement circuits. Traditional circuit-level decoding attempts to estimate the precise location of faults by constructing an extended Tanner…
Securing information transmission is critical today. However, with rapidly developing powerful quantum technologies, conventional cryptography techniques are becoming more prone to attacks each day. New techniques in the realm of quantum…
Two classes of turbo codes over high-order finite fields are introduced. The codes are derived from a particular protograph sub-ensemble of the (dv=2,dc=3) low-density parity-check code ensemble. A first construction is derived as a…
We introduce new reliability definitions for bit and check nodes. Maximizing global reliability, which is the sum reliability of all bit nodes, is shown to be equivalent to minimizing a decoding metric which is closely related to the…
An algorithm for constructing parity-check matrices of non-binary quasi-cyclic low-density parity-check (NB QC-LDPC) codes is proposed. The algorithm finds short cycles in the base matrix and tries to eliminate them by selecting the…
Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computation with constant overhead. Recent advancements have shown that qLDPC codes can outperform the quantum memory capability of…
In this paper, we investigate the performance of a class of spatially coupled codes, namely partially information coupled turbo codes (PIC-TCs) over the binary erasure channel (BEC). This class of codes enjoy flexible code rate adjustment…
Quantum low density parity check (qLDPC) codes, particularly bivariate bicycle (BB) codes, achieve competitive fault tolerance thresholds while offering substantially higher encoding rates than planar surface codes. However, their…
Cyclic codes have many applications in consumer electronics, communication and data storage systems due to their efficient encoding and decoding algorithms. An efficient approach to constructing cyclic codes is the sequence approach. In…
This article bridges the gap between two topics used in sharing an encryption key: (i) Key Consolidation, i.e., extracting two identical strings of bits from two information sources with similarities (common randomness). (ii) Quantum-safe…
In Proof-of-Work blockchains, difficulty algorithms serve the crucial purpose of maintaining a stable transaction throughput by dynamically adjusting the block difficulty in response to the miners' constantly changing computational power.…
Hypergraph product codes are a class of constant-rate quantum low-density parity-check (LDPC) codes equipped with a linear-time decoder called small-set-flip (SSF). This decoder displays sub-optimal performance in practice and requires very…
Generalized Tanner graphs have been implicitly studied by a number of authors under the rubric of generalized parity-check matrices. This work considers the conditioning of binary hidden variables in such models in order to break all cycles…
In many practical communication systems, one binary encoder/decoder pair is used to communicate over a set of parallel channels. Examples of this setup include multi-carrier transmission, rate-compatible puncturing of turbo-like codes, and…
McEliece encryption scheme which enjoys relatively small key sizes as well as a security reduction to hard problems of coding theory. Furthermore, it remains secure against a quantum adversary and is very well suited to low cost…
In this paper, we propose how to construct a reconciliation method for the BB84 Quantum Key Distribution (QKD) protocol. Theoretically, it is unconditionally secure because it is based on the quantum laws of physics, rather than the assumed…
For efficient modulation and error control coding, the deliberate flipping approach imposes the run-length-limited(RLL) constraint by bit error before recording. From the read side, a high coding rate limits the correcting capability of RLL…
Polar codes attract more and more attention of researchers in recent years, since its capacity achieving property. However, their error-correction performance under successive cancellation (SC) decoding is inferior to other modern channel…
The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcting code's efficiency, the syndrome extraction circuit's…
In this thesis, we study algebraic coding theory based McEliece-type cryptosystems over quasi-cyclic codes. The main goal of this thesis is to construct a cryptosystem that resists quantum Fourier sampling making it quantum secure. We…