230 research outputs found
A New Class of MDS Erasure Codes Based on Graphs
Maximum distance separable (MDS) array codes are XOR-based optimal erasure
codes that are particularly suitable for use in disk arrays. This paper
develops an innovative method to build MDS array codes from an elegant class of
nested graphs, termed \textit{complete-graph-of-rings (CGR)}. We discuss a
systematic and concrete way to transfer these graphs to array codes, unveil an
interesting relation between the proposed map and the renowned perfect
1-factorization, and show that the proposed CGR codes subsume B-codes as their
"contracted" codes. These new codes, termed \textit{CGR codes}, and their dual
codes are simple to describe, and require minimal encoding and decoding
complexity.Comment: in Proceeding of IEEE Global Communications Conference (GLOBECOM
Low-density MDS codes and factors of complete graphs
We present a class of array code of size nĂl, where l=2n or 2n+1, called B-Code. The distances of the B-Code and its dual are 3 and l-1, respectively. The B-Code and its dual are optimal in the sense that i) they are maximum-distance separable (MDS), ii) they have an optimal encoding property, i.e., the number of the parity bits that are affected by change of a single information bit is minimal, and iii) they have optimal length. Using a new graph description of the codes, we prove an equivalence relation between the construction of the B-Code (or its dual) and a combinatorial problem known as perfect one-factorization of complete graphs, thus obtaining constructions of two families of the B-Code and its dual, one of which is new. Efficient decoding algorithms are also given, both for erasure correcting and for error correcting. The existence of perfect one-factorizations for every complete graph with an even number of nodes is a 35 years long conjecture in graph theory. The construction of B-Codes of arbitrary odd length will provide an affirmative answer to the conjecture
Low-Density Parity-Check Codes for Nonergodic Block-Fading Channels
We solve the problem of designing powerful low-density parity-check (LDPC)
codes with iterative decoding for the block-fading channel. We first study the
case of maximum-likelihood decoding, and show that the design criterion is
rather straightforward. Unfortunately, optimal constructions for
maximum-likelihood decoding do not perform well under iterative decoding. To
overcome this limitation, we then introduce a new family of full-diversity LDPC
codes that exhibit near-outage-limit performance under iterative decoding for
all block-lengths. This family competes with multiplexed parallel turbo codes
suitable for nonergodic channels and recently reported in the literature.Comment: Submitted to the IEEE Transactions on Information Theor
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