Related papers: Efficient Near Maximum-Likelihood Reliability-Base…
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…
This paper is concerned with the ordered statistic decoding with local constraints (LC-OSD) of binary linear block codes, which is a near maximum-likelihood decoding algorithm. Compared with the conventional OSD, the LC-OSD significantly…
Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has attracted much attention in the research community in the past few years. LP decoding has been derived for binary and nonbinary linear codes. However, the most…
Quantum error correction (QEC) for fault-tolerant quantum computing requires a balanced decoding solution that offers high performance, low complexity, and low latency. However, the de facto standard, belief propagation (BP) combined with…
Efficient and scalable decoding of quantum codes is essential for high-performance quantum error correction. In this work, we introduce Reliable Subset Reduction (RSR), a reliability-driven preprocessing framework that leverages belief…
We examine LDPC codes decoded using linear programming (LP). Four contributions to the LP framework are presented. First, a new method of tightening the LP relaxation, and thus improving the LP decoder, is proposed. Second, we present an…
We propose a new type of short to moderate block-length, linear error-correcting codes, called moderate-density parity-check (MDPC) codes. The number of ones of the parity-check matrix of the codes presented is typically higher than the…
The equivalence of peeling decoding (PD) and Belief Propagation (BP) for low-density parity-check (LDPC) codes over the binary erasure channel is analyzed. Modifying the scheduling for PD, it is shown that exactly the same variable nodes…
We describe two implementations of the optimal error correction algorithm known as the maximum likelihood decoder (MLD) for the 2D surface code with a noiseless syndrome extraction. First, we show how to implement MLD exactly in time…
With the use of belief propagation (BP) decoding algorithm, low-density parity-check (LDPC) codes can achieve near-Shannon limit performance. In order to evaluate the error performance of LDPC codes, simulators running on CPUs are commonly…
In this work, we present an adaptive reliability-driven conditional innovation (AR-CID) decoding algorithm for low-density parity check (LDPC) codes. The proposed AR-CID decoding algorithm consists of one stage of message quality checking…
We present a new decoder for the surface code, which combines the accuracy of the tensor-network decoders with the efficiency and parallelism of the belief-propagation algorithm. Our main idea is to replace the expensive tensor-network…
In this paper, we propose a new class of bit flipping algorithms for low-density parity-check (LDPC) codes over the binary symmetric channel (BSC). Compared to the regular (parallel or serial) bit flipping algorithms, the proposed…
Due to the high error rate of qubits, detecting and correcting errors is essential for achieving fault-tolerant quantum computing (FTQC). Quantum low-density parity-check (QLDPC) codes are one of the most promising quantum error correction…
Belief propagation (BP) decoding of quantum low density parity check (QLDPC) codes is often implemented using overcomplete stabilizer (OS) representations, where redundant parity checks are introduced to improve finite length performance.…
In this paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, called interior point decoding, is designed for linear vector channels. The linear vector…
We propose a reduced complexity approach to pattern-based soft decoding of block codes. We start from the ORDEPT decoding algorithm which tests a list of partial error patterns organized in the order of their likelihood and attempts to…
Low-density parity-check (LDPC) codes are an important feature of several communication and storage applications, offering a flexible and effective method for error correction. These codes are computationally complex and require the…
In Linear Programming (LP) decoding of a Low-Density-Parity-Check (LDPC) code one minimizes a linear functional, with coefficients related to log-likelihood ratios, over a relaxation of the polytope spanned by the codewords \cite{03FWK}. In…
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…