Related papers: Quantized Iterative Message Passing Decoders with …
Quantum low-density parity-check (QLDPC) codes with asymptotically non-zero rates are prominent candidates for achieving fault-tolerant quantum computation, primarily due to their syndrome-measurement circuit's low operational depth.…
Iterative decoders for finite length quantum low-density parity-check (QLDPC) codes are attractive because their hardware complexity scales only linearly with the number of physical qubits. However, they are impacted by short cycles,…
In this study, we report that quantum quasi-cyclic low-density parity-check codes decoded via joint belief propagation (BP) exhibit steep error-rate curves, despite the presence of error floors. To the best of our knowledge, this is the…
In this paper, we propose a finite alphabet message passing algorithm for LDPC codes that replaces the standard min-sum variable node update rule by a mapping based on generic look-up tables. This mapping is designed in a way that maximizes…
In this paper, we propose an efficient method to reduce error floors in quantum error correction using non-binary low-density parity-check (LDPC) codes. We identify and classify cycle structures in the parity-check matrix where estimated…
This paper proposes a method for designing error correction codes by combining a known coding scheme with an autoencoder. Specifically, we integrate an LDPC code with a trained autoencoder to develop an error correction code for intractable…
In this paper, we analyze the error floor of quasi-cyclic (QC) low-density parity-check (LDPC) codes decoded by the sum-product algorithm (SPA) with row layered message-passing scheduling. For this, we develop a linear state-space model of…
We propose a quantized decoding algorithm for low- density parity-check codes where the variable node update rule of the standard min-sum algorithm is replaced with a look-up table (LUT) that is designed using an information-theoretic…
Iterative decoder failures of quantum low density parity check (QLDPC) codes are attributed to substructures in the code's graph, known as trapping sets, as well as degenerate errors that can arise in quantum codes. Failure inducing sets…
The error floor of LDPC is revisited as an effect of dynamic message behavior in the so-called absorption sets of the code. It is shown that if the signal growth in the absorption sets is properly balanced by the growth of set-external…
We investigate iterative low-resolution message-passing algorithms for quasi-cyclic LDPC codes with horizontal and vertical layered schedules. Coarse quantization and layered scheduling are highly relevant for hardware implementations to…
In this paper, we analyze the error floor of column layered decoders, also known as shuffled decoders, for low-density parity-check (LDPC) codes under saturating sum-product algorithm (SPA). To estimate the error floor, we evaluate the…
It is shown that dominant trapping sets of regular LDPC codes, so called absorption sets, undergo a two-phased dynamic behavior in the iterative message-passing decoding algorithm. Using a linear dynamic model for the iteration behavior of…
Finding optimal message quantization is a key requirement for low complexity belief propagation (BP) decoding. To this end, we propose a floating-point surrogate model that imitates quantization effects as additions of uniform noise, whose…
The error floor phenomenon, associated with iterative decoders, is one of the most significant limitations to the applications of low-density parity-check (LDPC) codes. A variety of techniques from code design to decoder implementation have…
This paper proposes two approaches for reducing the impact of the error floor phenomenon when decoding quantum low-density parity-check codes with belief propagation based algorithms. First, a low-complexity syndrome-based linear…
Quantum cryptography via key distribution mechanisms that utilize quantum entanglement between sender-receiver pairs will form the basis of future large-scale quantum networks. A key engineering challenge in such networks will be the…
In this paper, we propose a new class of quantized message-passing decoders for LDPC codes over the BSC. The messages take values (or levels) from a finite set. The update rules do not mimic belief propagation but instead are derived using…
Non-uniform message quantization techniques such as reconstruction-computation-quantization (RCQ) improve error-correction performance and decrease hardware complexity of low-density parity-check (LDPC) decoders that use a flooding…
We describe a family of instanton-based optimization methods developed recently for the analysis of the error floors of low-density parity-check (LDPC) codes. Instantons are the most probable configurations of the channel noise which result…