Related papers: Weighted Parity-Check Codes for Channels with Stat…
We present a theoretical method for a direct evaluation of the average and reliability error exponents in low-density parity-check error-correcting codes using methods of statistical physics. Results for the binary symmetric channel (BSC)…
This work considers the design of short non-binary low-density parity-check (LDPC) codes over finite fields of order m, for channels with phase noise. In particular, m-ary differential phase-shift keying (DPSK) modulated code symbols are…
A method for improving the performance of sparse-matrix based parity check codes is proposed, based on insight gained from methods of statistical physics. The advantages of the new approach are demonstrated on an existing encoding/decoding…
We investigate the use of Gallager's low-density parity-check (LDPC) codes in a broadcast channel, one of the fundamental models in network information theory. Combining linear codes is a standard technique in practical network…
The security of code-based cryptography relies primarily on the hardness of generic decoding with linear codes. The best generic decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of…
We present a constraint-coding scheme to correct asymmetric magnitude-$1$ errors in multi-level non-volatile memories. For large numbers of such errors, the scheme is shown to deliver better correction capability compared to known…
The construction of asymmetric error correcting codes is a topic that was studied extensively, however, the existing approach for code construction assumes that every codeword should tolerate $t$ asymmetric errors. Our main observation is…
We present parity measurements on a five-qubit lattice with connectivity amenable to the surface code quantum error correction architecture. Using all-microwave controls of superconducting qubits coupled via resonators, we encode the…
In this paper, we formulate a new problem to cope with the transmission of extra bits over an existing coded transmission link (referred to as coded payload link) without any cost of extra transmission energy or extra bandwidth. This is…
Quantum weight reduction procedures ease the implementation of quantum codes by sparsifying them, resulting in low-weight checks and low-degree qubits. However, to date, only few quantum weight reduction methods have been explored. In this…
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…
Linear codes have been an interesting subject of study for many years, as linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a class of…
The discovery of the family of balanced product codes was pivotal in the subsequent development of 'good' low density quantum error correcting codes that have optimal scaling of the key parameters of distance and storage density. We review…
We use a combination of analytical and numerical techniques to calculate the noise threshold and resource requirements for a linear optical quantum computing scheme based on parity-state encoding. Parity-state encoding is used at the lowest…
Much progress has been made on decoding algorithms for error-correcting codes in the last decade. In this article, we give an introduction to some fundamental results on iterative, message-passing algorithms for low-density parity check…
We introduce surface ZZZY codes, a novel family of quantum error-correcting codes designed for asymmetric channels. Derived from standard surface codes through tailored modification of generators, ZZZY codes can be decoded by the minimum…
In this letter, we analyse the properties of a maximum likelihood channel estimator based on the syndrome of a linear code. For the two examples of a binary symmetric channel and a binary input additive white Gaussian noise channel, we…
We study relationships between worst-case and random-noise properties of error correcting codes. More concretely, we consider connections between minimum distance, list decoding radius, and block error probability on noisy channels. A…
We present a two-step decoder for the parity code and evaluate its performance in code-capacity and faulty-measurement settings. For noiseless measurements, we find that the decoding problem can be reduced to a series of repetition codes…
The paper presents bounds on the achievable rates and the decoding complexity of low-density parity-check (LDPC) codes. It is assumed that the communication of these codes takes place over statistically independent parallel channels where…