87 research outputs found
New Decoding of Reed-Solomon Codes Based on FFT and Modular Approach
Decoding algorithms for Reed--Solomon (RS) codes are of great interest for
both practical and theoretical reasons. In this paper, an efficient algorithm,
called the modular approach (MA), is devised for solving the Welch--Berlekamp
(WB) key equation. By taking the MA as the key equation solver, we propose a
new decoding algorithm for systematic RS codes. For RS codes, where
is the code length and is the code dimension, the proposed decoding
algorithm has both the best asymptotic computational complexity and the smallest constant factor achieved to date. By
comparing the number of field operations required, we show that when decoding
practical RS codes, the new algorithm is significantly superior to the existing
methods in terms of computational complexity. When decoding the
RS code defined over , the new algorithm is 10 times
faster than a conventional syndrome-based method. Furthermore, the new
algorithm has a regular architecture and is thus suitable for hardware
implementation
Update-Efficient Regenerating Codes with Minimum Per-Node Storage
Regenerating codes provide an efficient way to recover data at failed nodes
in distributed storage systems. It has been shown that regenerating codes can
be designed to minimize the per-node storage (called MSR) or minimize the
communication overhead for regeneration (called MBR). In this work, we propose
a new encoding scheme for [n,d] error- correcting MSR codes that generalizes
our earlier work on error-correcting regenerating codes. We show that by
choosing a suitable diagonal matrix, any generator matrix of the [n,{\alpha}]
Reed-Solomon (RS) code can be integrated into the encoding matrix. Hence, MSR
codes with the least update complexity can be found. An efficient decoding
scheme is also proposed that utilizes the [n,{\alpha}] RS code to perform data
reconstruction. The proposed decoding scheme has better error correction
capability and incurs the least number of node accesses when errors are
present.Comment: Submitted to IEEE ISIT 201
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