584 research outputs found
Fast-Decodable Asymmetric Space-Time Codes from Division Algebras
Multiple-input double-output (MIDO) codes are important in the near-future
wireless communications, where the portable end-user device is physically small
and will typically contain at most two receive antennas. Especially tempting is
the 4 x 2 channel due to its immediate applicability in the digital video
broadcasting (DVB). Such channels optimally employ rate-two space-time (ST)
codes consisting of (4 x 4) matrices. Unfortunately, such codes are in general
very complex to decode, hence setting forth a call for constructions with
reduced complexity.
Recently, some reduced complexity constructions have been proposed, but they
have mainly been based on different ad hoc methods and have resulted in
isolated examples rather than in a more general class of codes. In this paper,
it will be shown that a family of division algebra based MIDO codes will always
result in at least 37.5% worst-case complexity reduction, while maintaining
full diversity and, for the first time, the non-vanishing determinant (NVD)
property. The reduction follows from the fact that, similarly to the Alamouti
code, the codes will be subsets of matrix rings of the Hamiltonian quaternions,
hence allowing simplified decoding. At the moment, such reductions are among
the best known for rate-two MIDO codes. Several explicit constructions are
presented and shown to have excellent performance through computer simulations.Comment: 26 pages, 1 figure, submitted to IEEE Trans. Inf. Theory, October
201
Construction of Block Orthogonal STBCs and Reducing Their Sphere Decoding Complexity
Construction of high rate Space Time Block Codes (STBCs) with low decoding
complexity has been studied widely using techniques such as sphere decoding and
non Maximum-Likelihood (ML) decoders such as the QR decomposition decoder with
M paths (QRDM decoder). Recently Ren et al., presented a new class of STBCs
known as the block orthogonal STBCs (BOSTBCs), which could be exploited by the
QRDM decoders to achieve significant decoding complexity reduction without
performance loss. The block orthogonal property of the codes constructed was
however only shown via simulations. In this paper, we give analytical proofs
for the block orthogonal structure of various existing codes in literature
including the codes constructed in the paper by Ren et al. We show that codes
formed as the sum of Clifford Unitary Weight Designs (CUWDs) or Coordinate
Interleaved Orthogonal Designs (CIODs) exhibit block orthogonal structure. We
also provide new construction of block orthogonal codes from Cyclic Division
Algebras (CDAs) and Crossed-Product Algebras (CPAs). In addition, we show how
the block orthogonal property of the STBCs can be exploited to reduce the
decoding complexity of a sphere decoder using a depth first search approach.
Simulation results of the decoding complexity show a 30% reduction in the
number of floating point operations (FLOPS) of BOSTBCs as compared to STBCs
without the block orthogonal structure.Comment: 16 pages, 7 figures; Minor changes in lemmas and construction
Outlaw distributions and locally decodable codes
Locally decodable codes (LDCs) are error correcting codes that allow for
decoding of a single message bit using a small number of queries to a corrupted
encoding. Despite decades of study, the optimal trade-off between query
complexity and codeword length is far from understood. In this work, we give a
new characterization of LDCs using distributions over Boolean functions whose
expectation is hard to approximate (in~~norm) with a small number of
samples. We coin the term `outlaw distributions' for such distributions since
they `defy' the Law of Large Numbers. We show that the existence of outlaw
distributions over sufficiently `smooth' functions implies the existence of
constant query LDCs and vice versa. We give several candidates for outlaw
distributions over smooth functions coming from finite field incidence
geometry, additive combinatorics and from hypergraph (non)expanders.
We also prove a useful lemma showing that (smooth) LDCs which are only
required to work on average over a random message and a random message index
can be turned into true LDCs at the cost of only constant factors in the
parameters.Comment: A preliminary version of this paper appeared in the proceedings of
ITCS 201
Generalized Silver Codes
For an transmit, receive antenna system (
system), a {\it{full-rate}} space time block code (STBC) transmits complex symbols per channel use. The well known Golden code is an
example of a full-rate, full-diversity STBC for 2 transmit antennas. Its
ML-decoding complexity is of the order of for square -QAM. The
Silver code for 2 transmit antennas has all the desirable properties of the
Golden code except its coding gain, but offers lower ML-decoding complexity of
the order of . Importantly, the slight loss in coding gain is negligible
compared to the advantage it offers in terms of lowering the ML-decoding
complexity. For higher number of transmit antennas, the best known codes are
the Perfect codes, which are full-rate, full-diversity, information lossless
codes (for ) but have a high ML-decoding complexity of the order
of (for , the punctured Perfect codes are
considered). In this paper, a scheme to obtain full-rate STBCs for
transmit antennas and any with reduced ML-decoding complexity of the
order of , is presented. The codes constructed are
also information lossless for , like the Perfect codes and allow
higher mutual information than the comparable punctured Perfect codes for . These codes are referred to as the {\it generalized Silver codes},
since they enjoy the same desirable properties as the comparable Perfect codes
(except possibly the coding gain) with lower ML-decoding complexity, analogous
to the Silver-Golden codes for 2 transmit antennas. Simulation results of the
symbol error rates for 4 and 8 transmit antennas show that the generalized
Silver codes match the punctured Perfect codes in error performance while
offering lower ML-decoding complexity.Comment: Accepted for publication in the IEEE Transactions on Information
Theory. This revised version has 30 pages, 7 figures and Section III has been
completely revise
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