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We derive two families of EA-QC quantum LDPC (EA-QC-QLDPC) codes by tiling permutation matrices of prime and composite orders. The unassisted portion of the Tanner graphs corresponding to these codes, constructed from two distinct classical…
Random (dv,dc)-regular LDPC codes are well-known to achieve the Shannon capacity of the binary symmetric channel (for sufficiently large dv and dc) under exponential time decoding. However, polynomial time algorithms are only known to…
Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…
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…
This paper presents a unifying framework to construct low-density parity-check (LDPC) codes with associated Tanner graphs of desired girth. Towards this goal, we highlight the role that a certain square matrix that appears in the product of…
Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. A traditional approach is to look for codes which simultaneously maximize error tolerance and minimize storage space consumption. However, this…
In this paper, we give a generalization on the error correcting capability of twisted centralizer codes obtained from a fixed rank 1 matrix. In particular, we fix the combinatorial matrix which is obtained by getting the linear combination…
The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcting code's efficiency, the syndrome extraction circuit's…
Because of their capacity-approaching performance, graph-based codes have a wide range of applications, including communications and storage. In these codes, unequal error protection (UEP) can offer performance gains with limited rate loss.…
In this paper, we study binary constrained codes that are resilient to bit-flip errors and erasures. In our first approach, we compute the sizes of constrained subcodes of linear codes. Since there exist well-known linear codes that achieve…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
This paper discusses scalability of standard genetic programming (GP) and the probabilistic incremental program evolution (PIPE). To investigate the need for both effective mixing and linkage learning, two test problems are considered:…
Vertex Cover parameterized by the solution size k is the quintessential fixed-parameter tractable problem. FPT algorithms are most interesting when the parameter is small. Several lower bounds on k are well-known, such as the maximum size…
We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances, we observe that the obtained bounds outperform all…
A linear-programming decoder for \emph{nonbinary} expander codes is presented. It is shown that the proposed decoder has the maximum-likelihood certificate properties. It is also shown that this decoder corrects any pattern of errors of a…
This paper focuses on error-correcting codes that can handle a predefined set of specific error patterns. The need for such codes arises in many settings of practical interest, including wireless communication and flash memory systems. In…
The relation between parity-check matrices of quasi-cyclic (QC) low-density parity-check (LDPC) codes and biadjacency matrices of bipartite graphs supports searching for powerful LDPC block codes. Using the principle of tailbiting, compact…
We describe a new parameterized family of symmetric error-correcting codes with low-density parity-check matrices (LDPC). Our codes can be described in two seemingly different ways. First, in relation to Reed-Muller codes: our codes are…
Distributed storage systems suffer from significant repair traffic generated due to frequent storage node failures. This paper shows that properly designed low-density parity-check (LDPC) codes can substantially reduce the amount of…
Due to their capacity approaching performance low-density parity-check (LDPC) codes gained a lot of attention in the last years. The parity-check matrix of the codes can be associated with a bipartite graph, called Tanner graph. To decrease…