3 research outputs found
Asymptotically MDS Array BP-XOR Codes
Belief propagation or message passing on binary erasure channels (BEC) is a
low complexity decoding algorithm that allows the recovery of message symbols
based on bipartite graph prunning process. Recently, array XOR codes have
attracted attention for storage systems due to their burst error recovery
performance and easy arithmetic based on Exclusive OR (XOR)-only logic
operations. Array BP-XOR codes are a subclass of array XOR codes that can be
decoded using BP under BEC. Requiring the capability of BP-decodability in
addition to Maximum Distance Separability (MDS) constraint on the code
construction process is observed to put an upper bound on the maximum
achievable code block length, which leads to the code construction process to
become a harder problem. In this study, we introduce asymptotically MDS array
BP-XOR codes that are alternative to exact MDS array BP-XOR codes to pave the
way for easier code constructions while keeping the decoding complexity low
with an asymptotically vanishing coding overhead. We finally provide and
analyze a simple code construction method that is based on discrete geometry to
fulfill the requirements of the class of asymptotically MDS array BP-XOR codes.Comment: 8 pages, 4 figures, to be submitte
Asymptotically MDS Array BP-XOR Codes
Belief propagation or message passing on binary erasure channels (BEC) is a
low complexity decoding algorithm that allows the recovery of message symbols
based on bipartite graph prunning process. Recently, array XOR codes have
attracted attention for storage systems due to their burst error recovery
performance and easy arithmetic based on Exclusive OR (XOR)-only logic
operations. Array BP-XOR codes are a subclass of array XOR codes that can be
decoded using BP under BEC. Requiring the capability of BP-decodability in
addition to Maximum Distance Separability (MDS) constraint on the code
construction process is observed to put an upper bound on the maximum
achievable code block length, which leads to the code construction process to
become a harder problem. In this study, we introduce asymptotically MDS array
BP-XOR codes that are alternative to exact MDS array BP-XOR codes to pave the
way for easier code constructions while keeping the decoding complexity low
with an asymptotically vanishing coding overhead. We finally provide and
analyze a simple code construction method that is based on discrete geometry to
fulfill the requirements of the class of asymptotically MDS array BP-XOR codes.Comment: 8 pages, 4 figures, to be submitte
Mojette transform based LDPC erasure correction codes for distributed storage systems
International audienceMojette Transform (MT) based erasure correction coding possesses extremely efficient encoding/decoding algorithms and demonstrate promising burst erasure recovery performance. MT codes are based on discrete geometry and provide redundancy through creating projections. Projections are made of smaller data structures called bins and are generated from a two dimensional convex-shaped data. For exact data recovery, only a subset of projections are needed by the decoder. We realize that the discrete geometry definition of MT erasure codes corresponds to creating structured/deterministic generator matrices. In this study, we show an alternative Low Density Parity Check (LDPC) code construction methodology through investigating parity check matrices of MT codes which shows sparseness as the blocklength of the code gets large. In a distributed storage setting, we also quantify the repair bandwidth and show that this novel interpretation can be used to facilitate bin-level local repairs