Related papers: Improved Decoding and Error Floor Analysis of Stai…
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…
High-rate product codes (PCs) and staircase codes (SCs) are ubiquitous codes in high-speed optical communication achieving near-capacity performance on the binary symmetric channel. Their success is mostly due to very efficient iterative…
We generalize staircase codes and tiled diagonal zipper codes, preserving their key properties while allowing each coded symbol to be protected by arbitrarily many component codewords rather than only two. This generalization which we term…
We propose a new strategy to decode color codes, which is based on the projection of the error onto three surface codes. This provides a method to transform every decoding algorithm of surface codes into a decoding algorithm of color codes.…
In this work, we show that polar belief propagation (BP) decoding exhibits an error floor behavior which is caused by clipping of the log-likelihood ratios (LLR). The error floor becomes more pronounced for clipping to smaller LLR-values.…
We propose two variants of staircase codes that resolve the issue of parity-propagation in their encoding process. The proposed codes provide a systematic way of terminating a staircase code after an arbitrary number of blocks. The class of…
We discuss how the loop calculus approach of [Chertkov, Chernyak '06], enhanced by the pseudo-codeword search algorithm of [Chertkov, Stepanov '06] and the facet-guessing idea from [Dimakis, Wainwright '06], improves decoding of graph based…
We propose a novel soft-aided hard-decision decoding algorithm for general product-like codes. It achieves error correcting performance similar to that of a soft-decision turbo decoder for staircase and OFEC codes, while maintaining a low…
Product codes (PCs) and staircase codes (SCCs) are conventionally decoded based on bounded distance decoding (BDD) of the component codes and iterating between row and column decoders. The performance of iterative BDD (iBDD) can be improved…
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…
The error floor phenomenon observed with LDPC codes and their graph-based, iterative, message-passing (MP) decoders is commonly attributed to the existence of error-prone substructures -- variously referred to as near codewords, trapping…
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…
The development of practical, high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing. Here we propose a decoder for the surface code that finds low-weight correction operators for errors produced…
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…
Floquet codes define fault-tolerant protocols through periodic measurement sequences that drive a dynamically evolving stabilizer group. They provide a natural framework for hardware supporting two-qubit parity measurements but no unitary…
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…
Polar codes are a class of linear block codes that provably achieves channel capacity, and have been selected as a coding scheme for $5^{\rm th}$ generation wireless communication standards. Successive-cancellation (SC) decoding of polar…
The color code is remarkable for its ability to perform fault-tolerant logic gates. This motivates the design of practical decoders that minimise the resource cost of color-code quantum computation. Here we propose a decoder for the planar…
Understanding brain function, constructing computational models and engineering neural prosthetics require assessing two problems, namely encoding and decoding, but their relation remains controversial. For decades, the encoding problem has…
Two-dimensional color codes are a promising candidate for fault-tolerant quantum computing, as they have high encoding rates, transversal implementation of logical Clifford gates, and resource-efficient magic state preparation schemes.…