79 research outputs found
Matched Metrics and Channels
The most common decision criteria for decoding are maximum likelihood
decoding and nearest neighbor decoding. It is well-known that maximum
likelihood decoding coincides with nearest neighbor decoding with respect to
the Hamming metric on the binary symmetric channel. In this work we study
channels and metrics for which those two criteria do and do not coincide for
general codes
Classification of poset-block spaces admitting MacWilliams-type identity
In this work we prove that a poset-block space admits a MacWilliams-type
identity if and only if the poset is hierarchical and at any level of the
poset, all the blocks have the same dimension. When the poset-block admits the
MacWilliams-type identity we explicit the relation between the weight
enumerators of a code and its dual.Comment: 8 pages, 1 figure. Submitted to IEEE Transactions on Information
Theor
Generalized weights and bounds for error probability over erasure channels
New upper and lower bounds for the error probability over an erasure channel
are provided, making use of Wei's generalized weights, hierarchy and spectra.
In many situations the upper and lower bounds coincide and this allows
improvement of existing bounds. Results concerning MDS and AMDS codes are
deduced from those bounds
Bounds for complexity of syndrome decoding for poset metrics
In this work we show how to decompose a linear code relatively to any given
poset metric. We prove that the complexity of syndrome decoding is determined
by a maximal (primary) such decomposition and then show that a refinement of a
partial order leads to a refinement of the primary decomposition. Using this
and considering already known results about hierarchical posets, we can
establish upper and lower bounds for the complexity of syndrome decoding
relatively to a poset metric.Comment: Submitted to ITW 201
The Packing Radius of a Code and Partitioning Problems: the Case for Poset Metrics
Until this work, the packing radius of a poset code was only known in the
cases where the poset was a chain, a hierarchy, a union of disjoint chains of
the same size, and for some families of codes. Our objective is to approach the
general case of any poset. To do this, we will divide the problem into two
parts.
The first part consists in finding the packing radius of a single vector. We
will show that this is equivalent to a generalization of a famous NP-hard
problem known as "the partition problem". Then, we will review the main results
known about this problem giving special attention to the algorithms to solve
it. The main ingredient to these algorithms is what is known as the
differentiating method, and therefore, we will extend it to the general case.
The second part consists in finding the vector that determines the packing
radius of the code. For this, we will show how it is sometimes possible to
compare the packing radius of two vectors without calculating them explicitly
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