187 research outputs found
An Adaptive Conditional Zero-Forcing Decoder with Full-diversity, Least Complexity and Essentially-ML Performance for STBCs
A low complexity, essentially-ML decoding technique for the Golden code and
the 3 antenna Perfect code was introduced by Sirianunpiboon, Howard and
Calderbank. Though no theoretical analysis of the decoder was given, the
simulations showed that this decoding technique has almost maximum-likelihood
(ML) performance. Inspired by this technique, in this paper we introduce two
new low complexity decoders for Space-Time Block Codes (STBCs) - the Adaptive
Conditional Zero-Forcing (ACZF) decoder and the ACZF decoder with successive
interference cancellation (ACZF-SIC), which include as a special case the
decoding technique of Sirianunpiboon et al. We show that both ACZF and ACZF-SIC
decoders are capable of achieving full-diversity, and we give sufficient
conditions for an STBC to give full-diversity with these decoders. We then show
that the Golden code, the 3 and 4 antenna Perfect codes, the 3 antenna Threaded
Algebraic Space-Time code and the 4 antenna rate 2 code of Srinath and Rajan
are all full-diversity ACZF/ACZF-SIC decodable with complexity strictly less
than that of their ML decoders. Simulations show that the proposed decoding
method performs identical to ML decoding for all these five codes. These STBCs
along with the proposed decoding algorithm outperform all known codes in terms
of decoding complexity and error performance for 2,3 and 4 transmit antennas.
We further provide a lower bound on the complexity of full-diversity
ACZF/ACZF-SIC decoding. All the five codes listed above achieve this lower
bound and hence are optimal in terms of minimizing the ACZF/ACZF-SIC decoding
complexity. Both ACZF and ACZF-SIC decoders are amenable to sphere decoding
implementation.Comment: 11 pages, 4 figures. Corrected a minor typographical erro
Full-Rate, Full-Diversity, Finite Feedback Space-Time Schemes with Minimum Feedback and Transmission Duration
In this paper a MIMO quasi static block fading channel with finite N-ary
delay-free, noise-free feedback is considered. The transmitter uses a set of N
Space-Time Block Codes (STBCs), one corresponding to each of the N possible
feedback values, to encode and transmit information. The feedback function used
at the receiver and the N component STBCs used at the transmitter together
constitute a Finite Feedback Scheme (FFS). Although a number of FFSs are
available in the literature that provably achieve full-diversity, there is no
known universal criterion to determine whether a given arbitrary FFS achieves
full-diversity or not. Further, all known full-diversity FFSs for T<N_t where
N_t is the number of transmit antennas, have rate at the most 1. In this paper
a universal necessary condition for any FFS to achieve full-diversity is given,
using which the notion of Feedback-Transmission duration optimal (FT-Optimal)
FFSs - schemes that use minimum amount of feedback N given the transmission
duration T, and minimum transmission duration given the amount of feedback to
achieve full-diversity - is introduced. When there is no feedback (N=1) an
FT-optimal scheme consists of a single STBC with T=N_t, and the universal
necessary condition reduces to the well known necessary and sufficient
condition for an STBC to achieve full-diversity: every non-zero codeword
difference matrix of the STBC must be of rank N_t. Also, a sufficient condition
for full-diversity is given for the FFSs in which the component STBC with the
largest minimum Euclidean distance is chosen. Using this sufficient condition
full-rate (rate N_t) full-diversity FT-Optimal schemes are constructed for all
(N_t,T,N) with NT=N_t. These are the first full-rate full-diversity FFSs
reported in the literature for T<N_t. Simulation results show that the new
schemes have the best error performance among all known FFSs.Comment: 12 pages, 5 figures, 1 tabl
Capacity of Coded Index Modulation
We consider the special case of index coding over the Gaussian broadcast
channel where each receiver has prior knowledge of a subset of messages at the
transmitter and demands all the messages from the source. We propose a
concatenated coding scheme for this problem, using an index code for the
Gaussian channel as an inner code/modulation to exploit side information at the
receivers, and an outer code to attain coding gain against the channel noise.
We derive the capacity region of this scheme by viewing the resulting channel
as a multiple-access channel with many receivers, and relate it to the 'side
information gain' -- which is a measure of the advantage of a code in utilizing
receiver side information -- of the inner index code/modulation. We demonstrate
the utility of the proposed architecture by simulating the performance of an
index code/modulation concatenated with an off-the-shelf convolutional code
through bit-interleaved coded-modulation.Comment: To appear in Proc. IEEE Int. Symp. Inf. Theory (ISIT) 2015, Hong
Kong, Jun. 2015. 5 pages, 4 figure
Asymptotically-Optimal, Fast-Decodable, Full-Diversity STBCs
For a family/sequence of STBCs , with
increasing number of transmit antennas , with rates complex symbols
per channel use (cspcu), the asymptotic normalized rate is defined as . A family of STBCs is said to be
asymptotically-good if the asymptotic normalized rate is non-zero, i.e., when
the rate scales as a non-zero fraction of the number of transmit antennas, and
the family of STBCs is said to be asymptotically-optimal if the asymptotic
normalized rate is 1, which is the maximum possible value. In this paper, we
construct a new class of full-diversity STBCs that have the least ML decoding
complexity among all known codes for any number of transmit antennas and
rates cspcu. For a large set of pairs, the new codes
have lower ML decoding complexity than the codes already available in the
literature. Among the new codes, the class of full-rate codes () are
asymptotically-optimal and fast-decodable, and for have lower ML decoding
complexity than all other families of asymptotically-optimal, fast-decodable,
full-diversity STBCs available in the literature. The construction of the new
STBCs is facilitated by the following further contributions of this paper:(i)
For , we construct -group ML-decodable codes with rates greater than
one cspcu. These codes are asymptotically-good too. For , these are the
first instances of -group ML-decodable codes with rates greater than
cspcu presented in the literature. (ii) We construct a new class of
fast-group-decodable codes for all even number of transmit antennas and rates
.(iii) Given a design with full-rank linear dispersion
matrices, we show that a full-diversity STBC can be constructed from this
design by encoding the real symbols independently using only regular PAM
constellations.Comment: 16 pages, 3 tables. The title has been changed.The class of
asymptotically-good multigroup ML decodable codes has been extended to a
broader class of number of antennas. New fast-group-decodable codes and
asymptotically-optimal, fast-decodable codes have been include
Codes for Updating Linear Functions over Small Fields
We consider a point-to-point communication scenario where the receiver
maintains a specific linear function of a message vector over a finite field.
When the value of the message vector undergoes a sparse update, the transmitter
broadcasts a coded version of the modified message while the receiver uses this
codeword and the current value of the linear function to update its contents.
It is assumed that the transmitter has access to the modified message but is
unaware of the exact difference vector between the original and modified
messages. Under the assumption that the difference vector is sparse and that
its Hamming weight is at the most a known constant, the objective is to design
a linear code with as small a codelength as possible that allows successful
update of the linear function at the receiver. This problem is motivated by
applications to distributed data storage systems. Recently, Prakash and Medard
derived a lower bound on the codelength, which is independent of the size of
the underlying finite field, and provided constructions that achieve this bound
if the size of the finite field is sufficiently large. However, this
requirement on the field size can be prohibitive for even moderate values of
the system parameters. In this paper, we provide a field-size aware analysis of
the function update problem, including a tighter lower bound on the codelength,
and design codes that trade-off the codelength for a smaller field size
requirement. We first characterize the family of function update problems where
linear coding can provide reduction in codelength compared to a naive
transmission scheme. We then provide field-size dependent bounds on the optimal
codelength, and construct coding schemes when the receiver maintains linear
functions of striped message vector. Finally, we show that every function
update problem is equivalent to a generalized index coding problem.Comment: Keywords: distributed storage systems, function update problem, index
coding, side informatio
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