107,057 research outputs found
Binary and Ternary Quasi-perfect Codes with Small Dimensions
The aim of this work is a systematic investigation of the possible parameters
of quasi-perfect (QP) binary and ternary linear codes of small dimensions and
preparing a complete classification of all such codes. First we give a list of
infinite families of QP codes which includes all binary, ternary and quaternary
codes known to is. We continue further with a list of sporadic examples of
binary and ternary QP codes. Later we present the results of our investigation
where binary QP codes of dimensions up to 14 and ternary QP codes of dimensions
up to 13 are classified.Comment: 4 page
Results on Binary Linear Codes With Minimum Distance 8 and 10
All codes with minimum distance 8 and codimension up to 14 and all codes with
minimum distance 10 and codimension up to 18 are classified. Nonexistence of
codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new
exact bounds for binary linear codes. Primarily two algorithms considering the
dual codes are used, namely extension of dual codes with a proper coordinate,
and a fast algorithm for finding a maximum clique in a graph, which is modified
to find a maximum set of vectors with the right dependency structure.Comment: Submitted to the IEEE Transactions on Information Theory, May 2010 To
be presented at the ACCT 201
QPSK Block-Modulation Codes for Unequal Error Protection
Unequal error protection (UEP) codes find applications in broadcast channels, as well as in other digital communication systems, where messages have different degrees of importance. Binary linear UEP (LUEP) codes combined with a Gray mapped QPSK signal set are used to obtain new efficient QPSK block-modulation codes for unequal error protection. Several examples of QPSK modulation codes that have the same minimum squared Euclidean distance as the best QPSK modulation codes, of the same rate and length, are given. In the new constructions of QPSK block-modulation codes, even-length binary LUEP codes are used. Good even-length binary LUEP codes are obtained when shorter binary linear codes are combined using either the well-known |uÂŻ|uÂŻ+vÂŻ|-construction or the so-called construction X. Both constructions have the advantage of resulting in optimal or near-optimal binary LUEP codes of short to moderate lengths, using very simple linear codes, and may be used as constituent codes in the new constructions. LUEP codes lend themselves quite naturally to multistage decoding up to their minimum distance, using the decoding of component subcodes. A new suboptimal two-stage soft-decision decoding of LUEP codes is presented and its application to QPSK block-modulation codes for UEP illustrated
Code Design for Non-Coherent Detection of Frame Headers in Precoded Satellite Systems
In this paper we propose a simple method for generating short-length
rate-compatible codes over that are robust to non-coherent
detection for -PSK constellations. First, a greedy algorithm is used to
construct a family of rotationally invariant codes for a given constellation.
Then, by properly modifying such codes we obtain codes that are robust to
non-coherent detection. We briefly discuss the optimality of the constructed
codes for special cases of BPSK and QPSK constellations. Our method provides an
upper bound for the length of optimal codes with a given desired non-coherent
distance. We also derive a simple asymptotic upper bound on the frame error
rate (FER) of such codes and provide the simulation results for a selected set
of proposed codes. Finally, we briefly discuss the problem of designing binary
codes that are robust to non-coherent detection for QPSK constellation.Comment: 11 pages, 5 figure
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