3,887 research outputs found
A Unified Coded Deep Neural Network Training Strategy Based on Generalized PolyDot Codes for Matrix Multiplication
This paper has two contributions. First, we propose a novel coded matrix
multiplication technique called Generalized PolyDot codes that advances on
existing methods for coded matrix multiplication under storage and
communication constraints. This technique uses "garbage alignment," i.e.,
aligning computations in coded computing that are not a part of the desired
output. Generalized PolyDot codes bridge between Polynomial codes and MatDot
codes, trading off between recovery threshold and communication costs. Second,
we demonstrate that Generalized PolyDot can be used for training large Deep
Neural Networks (DNNs) on unreliable nodes prone to soft-errors. This requires
us to address three additional challenges: (i) prohibitively large overhead of
coding the weight matrices in each layer of the DNN at each iteration; (ii)
nonlinear operations during training, which are incompatible with linear
coding; and (iii) not assuming presence of an error-free master node, requiring
us to architect a fully decentralized implementation without any "single point
of failure." We allow all primary DNN training steps, namely, matrix
multiplication, nonlinear activation, Hadamard product, and update steps as
well as the encoding/decoding to be error-prone. We consider the case of
mini-batch size , as well as , leveraging coded matrix-vector
products, and matrix-matrix products respectively. The problem of DNN training
under soft-errors also motivates an interesting, probabilistic error model
under which a real number MDS code is shown to correct errors
with probability as compared to for the
more conventional, adversarial error model. We also demonstrate that our
proposed strategy can provide unbounded gains in error tolerance over a
competing replication strategy and a preliminary MDS-code-based strategy for
both these error models.Comment: Presented in part at the IEEE International Symposium on Information
Theory 2018 (Submission Date: Jan 12 2018); Currently under review at the
IEEE Transactions on Information Theor
RS + LDPC-Staircase Codes for the Erasure Channel: Standards, Usage and Performance
Application-Level Forward Erasure Correction (AL-FEC) codes are a key element of telecommunication systems. They are used to recover from packet losses when retransmission are not feasible and to optimize the large scale distribution of contents. In this paper we introduce Reed-Solomon/LDPCStaircase codes, two complementary AL-FEC codes that have recently been recognized as superior to Raptor codes in the context of the 3GPP-eMBMS call for technology [1]. After a brief introduction to the codes, we explain how to design high performance codecs which is a key aspect when targeting embedded systems with limited CPU/battery capacity. Finally we present the performances of these codes in terms of erasure correction capabilities and encoding/decoding speed, taking advantage of the 3GPP-eMBMS results where they have been ranked first
Error Correction for Index Coding With Coded Side Information
Index coding is a source coding problem in which a broadcaster seeks to meet
the different demands of several users, each of whom is assumed to have some
prior information on the data held by the sender. If the sender knows its
clients' requests and their side-information sets, then the number of packet
transmissions required to satisfy all users' demands can be greatly reduced if
the data is encoded before sending. The collection of side-information indices
as well as the indices of the requested data is described as an instance of the
index coding with side-information (ICSI) problem. The encoding function is
called the index code of the instance, and the number of transmissions employed
by the code is referred to as its length. The main ICSI problem is to determine
the optimal length of an index code for and instance. As this number is hard to
compute, bounds approximating it are sought, as are algorithms to compute
efficient index codes. Two interesting generalizations of the problem that have
appeared in the literature are the subject of this work. The first of these is
the case of index coding with coded side information, in which linear
combinations of the source data are both requested by and held as users'
side-information. The second is the introduction of error-correction in the
problem, in which the broadcast channel is subject to noise.
In this paper we characterize the optimal length of a scalar or vector linear
index code with coded side information (ICCSI) over a finite field in terms of
a generalized min-rank and give bounds on this number based on constructions of
random codes for an arbitrary instance. We furthermore consider the length of
an optimal error correcting code for an instance of the ICCSI problem and
obtain bounds on this number, both for the Hamming metric and for rank-metric
errors. We describe decoding algorithms for both categories of errors
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