相关论文: Near Maximum-Likelihood Performance of Some New Cy…

In his Ph.D. disseration, Feldman and his collaborators define the linear programming decoder for binary linear codes, which is a linear programming relaxation of the maximum-likelihood decoding problem. This decoder does not, in general,…

We consider spatially coupled low-density parity-check codes with finite smoothing parameters. A finite smoothing parameter is important for designing practical codes that are decoded using low-complexity windowed decoders. By optimizing…

In this letter, we present a hybrid iterative decoder for non-binary low density parity check (LDPC) codes over binary erasure channel (BEC), based on which the recursion of the erasure probability is derived to design non-binary LDPC codes…

One of the most important and challenging problems in coding theory is to construct codes with best possible parameters and properties. The class of quasi-cyclic (QC) codes is known to be fertile to produce such codes. Focusing on QC codes…

Recent developments in decoding of Tanner codes with maximum-likelihood certificates are based on a sufficient condition called local-optimality. We define hierarchies of locally-optimal codewords with respect to two parameters. One…

A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudo-random nature, and the new…

This study proposes an explicit construction method for quantum quasi-cyclic low-density parity-check (QC-LDPC) codes with a girth of 12. The proposed method designs parity-check matrices that maximize the girth while maintaining an…

The performance of iterative decoding techniques for linear block codes correcting erasures depends very much on the sizes of the stopping sets associated with the underlying Tanner graph, or, equivalently, the parity-check matrix…

Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, almost perfect nonlinear…

We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman et al. succeeds in…

In this paper, we develop a new decoding algorithm of a binary linear codes for symbol-pair read channels. Symbol-pair read channel has recently been introduced by Cassuto and Blaum to model channels with high write resolution but low read…

While low-density parity-check (LDPC) codes are near capacity-achieving when paired with iterative decoders, these decoders may not output a codeword due to the existence of pseudocodewords. Thus, pseudocodewords have been studied to give…

Spatially-coupled low-density parity-check codes attract much attention due to their capacity-achieving performance and a memory-efficient sliding-window decoding algorithm. On the other hand, the encoder needs to solve large linear…

Surface codes exploit topological protection to increase error resilience in quantum computing devices and can in principle be implemented in existing hardware. They are one of the most promising candidates for active error correction, not…

As a subclass of linear codes, cyclic codes have efficient encoding and decoding algorithms, so they are widely used in many areas such as consumer electronics, data storage systems and communication systems. In this paper, we give a…

Error probability distribution associated with a given Clifford measurement circuit is described exactly in terms of the circuit error-equivalence group, or the circuit subsystem code previously introduced by Bacon, Flammia, Harrow, and…

I will show that there is a deep relation between error-correction codes and certain mathematical models of spin glasses. In particular minimum error probability decoding is equivalent to finding the ground state of the corresponding spin…

For a number of quantum channels of interest, phase-flip errors occur far more frequently than bit-flip errors. When transmitting across these asymmetric channels, the decoding error rate can be reduced by tailoring the code used to the…

A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…