5 research outputs found
Optimal strongly conflict-avoiding codes of even length and weight three
Strongly conflict-avoiding codes (SCACs) are employed in a slot-asynchronous
multiple-access collision channel without feedback to guarantee that each
active user can send at least one packet successfully in the worst case within
a fixed period of time. Assume all users are assigned distinct codewords, the
number of codewords in an SCAC is equal to the number of potential users that
can be supported. SCACs have different combinatorial structure compared with
conflict-avoiding codes (CACs) due to additional collisions incurred by
partially overlapped transmissions. In this paper, we establish upper bounds on
the size of SCACs of even length and weight three. Furthermore, it is shown
that some optimal CACs can be used to construct optimal SCACs of weight three.Comment: 18 pages, 1 figure. Submitted to Designs, Codes and Cryptography. 1st
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A new upper bound and optimal constructions of equi-difference conflict-avoiding codes on constant weight
Conflict-avoiding codes (CACs) have been used in multiple-access collision
channel without feedback. The size of a CAC is the number of potential users
that can be supported in the system. A code with maximum size is called
optimal. The use of an optimal CAC enables the largest possible number of
asynchronous users to transmit information efficiently and reliably. In this
paper, a new upper bound on the maximum size of arbitrary equi-difference CAC
is presented. Furthermore, three optimal constructions of equi-difference CACs
are also given. One is a generalized construction for prime length and
the other two are for two-prime length .Comment: 1
Multichannel Conflict-Avoiding Codes of Weights Three and Four
Conflict-avoiding codes (CACs) were introduced by Levenshtein as a
single-channel transmission scheme for a multiple-access collision channel
without feedback. When the number of simultaneously active source nodes is less
than or equal to the weight of a CAC, it is able to provide a hard guarantee
that each active source node transmits at least one packet successfully within
a fixed time duration, no matter what the relative time offsets between the
source nodes are. In this paper, we extend CACs to multichannel CACs for
providing such a hard guarantee over multiple orthogonal channels. Upper bounds
on the number of codewords for multichannel CACs of weights three and four are
derived, and constructions that are optimal with respect to these bounds are
presented.Comment: 12 pages. Accepted for publication in IEEE Transaction on Information
Theor
Optimal -D -optical orthogonal codes and related equi-difference conflict avoiding codes
This paper focuses on constructions for optimal -D -optical orthogonal codes with . An upper
bound on the size of such codes is established. It relies heavily on the size
of optimal equi-difference -D -optical orthogonal codes, which is
closely related to optimal equi-difference conflict avoiding codes with weight
. The exact number of codewords of an optimal -D -optical orthogonal code is determined for , , and , or or
Optimal optical orthogonal signature pattern codes with weight three and cross-correlation constraint one
Optical orthogonal signature pattern codes (OOSPCs) have attracted wide
attention as signature patterns of spatial optical code division multiple
access networks. In this paper, an improved upper bound on the size of an
-OOSPC with is established. The exact
number of codewords of an optimal -OOSPC is determined for
any positive integers and .Comment: To appear in Designs, Codes and Cryptography; According to the
referees' comments, the proof of Theorem 1.3 was removed to the current arXiv
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