34 research outputs found
Codes With Hierarchical Locality
In this paper, we study the notion of {\em codes with hierarchical locality}
that is identified as another approach to local recovery from multiple
erasures. The well-known class of {\em codes with locality} is said to possess
hierarchical locality with a single level. In a {\em code with two-level
hierarchical locality}, every symbol is protected by an inner-most local code,
and another middle-level code of larger dimension containing the local code. We
first consider codes with two levels of hierarchical locality, derive an upper
bound on the minimum distance, and provide optimal code constructions of low
field-size under certain parameter sets. Subsequently, we generalize both the
bound and the constructions to hierarchical locality of arbitrary levels.Comment: 12 pages, submitted to ISIT 201
Maximally Recoverable Codes with Hierarchical Locality
Maximally recoverable codes are a class of codes which recover from all
potentially recoverable erasure patterns given the locality constraints of the
code. In earlier works, these codes have been studied in the context of codes
with locality. The notion of locality has been extended to hierarchical
locality, which allows for locality to gradually increase in levels with the
increase in the number of erasures. We consider the locality constraints
imposed by codes with two-level hierarchical locality and define maximally
recoverable codes with data-local and local hierarchical locality. We derive
certain properties related to their punctured codes and minimum distance. We
give a procedure to construct hierarchical data-local MRCs from hierarchical
local MRCs. We provide a construction of hierarchical local MRCs for all
parameters. For the case of one global parity, we provide a different
construction of hierarchical local MRC over a lower field size.Comment: 6 pages, accepted to National Conference of Communications (NCC) 201
Algebraic hierarchical locally recoverable codes with nested affine subspace recovery
Codes with locality, also known as locally recoverable codes, allow for
recovery of erasures using proper subsets of other coordinates. Theses subsets
are typically of small cardinality to promote recovery using limited network
traffic and other resources. Hierarchical locally recoverable codes allow for
recovery of erasures using sets of other symbols whose sizes increase as needed
to allow for recovery of more symbols. In this paper, we construct codes with
hierarchical locality from a geometric perspective, using fiber products of
curves. We demonstrate how the constructed hierarchical codes can be viewed as
punctured subcodes of Reed-Muller codes. This point of view provides natural
structures for local recovery at each level in the hierarchy
A Study on the Impact of Locality in the Decoding of Binary Cyclic Codes
In this paper, we study the impact of locality on the decoding of binary
cyclic codes under two approaches, namely ordered statistics decoding (OSD) and
trellis decoding. Given a binary cyclic code having locality or availability,
we suitably modify the OSD to obtain gains in terms of the Signal-To-Noise
ratio, for a given reliability and essentially the same level of decoder
complexity. With regard to trellis decoding, we show that careful introduction
of locality results in the creation of cyclic subcodes having lower maximum
state complexity. We also present a simple upper-bounding technique on the
state complexity profile, based on the zeros of the code. Finally, it is shown
how the decoding speed can be significantly increased in the presence of
locality, in the moderate-to-high SNR regime, by making use of a quick-look
decoder that often returns the ML codeword.Comment: Extended version of a paper submitted to ISIT 201