منابع مشابه
Ja n 20 06 Improved Nearly - MDS Expander Codes ∗
A construction of expander codes is presented with the following three properties: (i) the codes lie close to the Singleton bound, (ii) they can be encoded in time complexity that is linear in their code length, and (iii) they have a linear-time bounded-distance decoder. By using a version of the decoder that corrects also erasures, the codes can replace MDS outer codes in concatenated construc...
متن کاملNearly MDS expander codes with reduced alphabet size
Recently, Roth and Skachek proposed two methods for constructing nearly maximum-distance separable (MDS) expander codes. We show that through the simple modification of using mixed-alphabet codes derived from MDS codes as constituent codes in their code designs, one can obtain nearly MDS codes of significantly smaller alphabet size, albeit at the expense of a (very slight) reduction in code rate.
متن کاملGradient Coding from Cyclic MDS Codes and Expander Graphs
Gradient Descent, and its variants, are a popular method for solving empirical risk minimization problems in machine learning. However, if the size of the training set is large, a computational bottleneck is the computation of the gradient, and hence, it is common to distribute the training set among worker nodes. Doing this in a synchronous fashion faces yet another challenge of stragglers (i....
متن کاملExpander Codes
We present a new class of asymptotically good, linear error-correcting codes based upon expander graphs. These codes have linear time sequential decoding algorithms , logarithmic time parallel decoding algorithms with a linear number of processors, and are simple to understand. We present both randomized and explicit constructions for some of these codes. Experimental results demonstrate the ex...
متن کاملOn expander codes
Expander codes count among the numerous applications of expander graphs. The term was first coined by Sipser and Spielman when they showed how expander graphs can be used to devise error-correcting codes with large blocklengths that can correct efficiently a constant fraction of errors. This approach has since proved to be a fertile avenue of research that provides insight both into modern iter...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2006
ISSN: 0018-9448
DOI: 10.1109/tit.2006.878232