This paper proposes to construct binary array codes from nonbinary codes by binary matrix dispersion. Thanks to their low-density and quasi-cyclic generator matrices, thesebinary dispersed array codes(BDACs) enjoy low encoding complexity. Their reconstruction property is characterized through matrix transformation. Several explicit constructions of BDACs from minimum-bandwidth regenerating codes, piggybacking codes, and locally recoverable codes are presented, as well as their similar single-node repair strategies to their nonbinary counterparts.

MOTIVATION: Combinatorial pooling schemes have enabled the measurement of thousands of experiments in a small number of reactions. This efficiency is achieved by distributing the items to be measured across multiple reaction units called pools. However, current methods for the design of pooling schemes do not adequately address the need for balanced item distribution across pools, a property particularly important for biological applications. RESULTS: Here, we introduce balanced constant-weight Gray codes for detecting consecutive positives (DCP-CWGCs) for the efficient construction of combinatorial pooling schemes. Balanced DCP-CWGCs ensure uniform item distribution across pools, allow for the identification of consecutive positive items such as overlapping biological sequences, and enable error detection by ensuring a constant number of tests on each item and pair of consecutive items. For the efficient construction of balanced DCP-CWGCs, we have released an open-source python package codePUB, with implementations of the two core algorithms: a branch-and-bound algorithm (BBA) and a recursive combination with BBA (rcBBA). Simulations using codePUB show that our algorithms can construct long, balanced DCP-CWGCs that allow for error detection in tractable runtime. AVAILABILITY AND IMPLEMENTATION: The source code of codePUB is available at https://github.com/meyer-lab-cshl/codepub, with detailed documentation at https://codepub.readthedocs.io/.

This paper proposes to construct binary array codes from non-binary codes by binary matrix dispersion. Thanks to their low-density and quasi-cyclic (QC) generator matrices, the proposed codes enjoy low encoding complexity, about$1/(m+1)$of the XOR operations used in their counterparts over$\mathbf{G F}\left(2^m\right)$. Their maximum distance separable (MDS) property and repair can be efficiently analyzed via matrix transformation. The MDS property is ensured by introducing Vandermonde upper triangular form and pre-processing. Moreover, the efficient repair can be guaranteed by applying a matrix mapping called all-one superposition on the associated matrices. Analysis indicates that their code rate and repair ratio asymptotically approach those of their non-binary counterparts.

In this paper, we show how to partition K users in a coded caching domain into L groups to reduce the complexity from O(2K) to [EQUATION]. We first show that the negative effects of the heterogeneity of cache sizes and partitioning on coded caching performance neutralize each other, which is the theoretical foundation of our partitioning schemes. We then prove the submodularity of the coded caching traffic volume function, based on which we develop a partition algorithm for minimizing the traffic volume. We show that the approximation ratio of proposed algorithm is better than the state-of-art result. Moreover, we develop a rounding algorithm to obtain the final partition based on Lovász extension, which resolves the issue of unbalanced partition. We implement our schemes in a testbed and validate our analysis and design with experiment results.