612 research outputs found

### MMSE Optimal Algebraic Space-Time Codes

Design of Space-Time Block Codes (STBCs) for Maximum Likelihood (ML)
reception has been predominantly the main focus of researchers. However, the ML
decoding complexity of STBCs becomes prohibitive large as the number of
transmit and receive antennas increase. Hence it is natural to resort to a
suboptimal reception technique like linear Minimum Mean Squared Error (MMSE)
receiver. Barbarossa et al and Liu et al have independently derived necessary
and sufficient conditions for a full rate linear STBC to be MMSE optimal, i.e
achieve least Symbol Error Rate (SER). Motivated by this problem, certain
existing high rate STBC constructions from crossed product algebras are
identified to be MMSE optimal. Also, it is shown that a certain class of codes
from cyclic division algebras which are special cases of crossed product
algebras are MMSE optimal. Hence, these STBCs achieve least SER when MMSE
reception is employed and are fully diverse when ML reception is employed.Comment: 5 pages, 1 figure, journal version to appear in IEEE Transactions on
Wireless Communications. Conference version appeared in NCC 2007, IIT Kanpur,
Indi

### Algebraic Distributed Space-Time Codes with Low ML Decoding Complexity

"Extended Clifford algebras" are introduced as a means to obtain low ML
decoding complexity space-time block codes. Using left regular matrix
representations of two specific classes of extended Clifford algebras, two
systematic algebraic constructions of full diversity Distributed Space-Time
Codes (DSTCs) are provided for any power of two number of relays. The left
regular matrix representation has been shown to naturally result in space-time
codes meeting the additional constraints required for DSTCs. The DSTCs so
constructed have the salient feature of reduced Maximum Likelihood (ML)
decoding complexity. In particular, the ML decoding of these codes can be
performed by applying the lattice decoder algorithm on a lattice of four times
lesser dimension than what is required in general. Moreover these codes have a
uniform distribution of power among the relays and in time, thus leading to a
low Peak to Average Power Ratio at the relays.Comment: 5 pages, no figures. To appear in Proceedings of IEEE ISIT 2007,
Nice, Franc

### STBCs from Representation of Extended Clifford Algebras

A set of sufficient conditions to construct $\lambda$-real symbol Maximum
Likelihood (ML) decodable STBCs have recently been provided by Karmakar et al.
STBCs satisfying these sufficient conditions were named as Clifford Unitary
Weight (CUW) codes. In this paper, the maximal rate (as measured in complex
symbols per channel use) of CUW codes for $\lambda=2^a,a\in\mathbb{N}$ is
obtained using tools from representation theory. Two algebraic constructions of
codes achieving this maximal rate are also provided. One of the constructions
is obtained using linear representation of finite groups whereas the other
construction is based on the concept of right module algebra over
non-commutative rings. To the knowledge of the authors, this is the first paper
in which matrices over non-commutative rings is used to construct STBCs. An
algebraic explanation is provided for the 'ABBA' construction first proposed by
Tirkkonen et al and the tensor product construction proposed by Karmakar et al.
Furthermore, it is established that the 4 transmit antenna STBC originally
proposed by Tirkkonen et al based on the ABBA construction is actually a single
complex symbol ML decodable code if the design variables are permuted and
signal sets of appropriate dimensions are chosen.Comment: 5 pages, no figures, To appear in Proceedings of IEEE ISIT 2007,
Nice, Franc

### Noncoherent Low-Decoding-Complexity Space-Time Codes for Wireless Relay Networks

The differential encoding/decoding setup introduced by Kiran et al, Oggier et
al and Jing et al for wireless relay networks that use codebooks consisting of
unitary matrices is extended to allow codebooks consisting of scaled unitary
matrices. For such codebooks to be used in the Jing-Hassibi protocol for
cooperative diversity, the conditions that need to be satisfied by the relay
matrices and the codebook are identified. A class of previously known rate one,
full diversity, four-group encodable and four-group decodable Differential
Space-Time Codes (DSTCs) is proposed for use as Distributed DSTCs (DDSTCs) in
the proposed set up. To the best of our knowledge, this is the first known low
decoding complexity DDSTC scheme for cooperative wireless networks.Comment: 5 pages, no figures. To appear in Proceedings of IEEE ISIT 2007,
Nice, Franc

### Signal Set Design for Full-Diversity Low-Decoding-Complexity Differential Scaled-Unitary STBCs

The problem of designing high rate, full diversity noncoherent space-time
block codes (STBCs) with low encoding and decoding complexity is addressed.
First, the notion of $g$-group encodable and $g$-group decodable linear STBCs
is introduced. Then for a known class of rate-1 linear designs, an explicit
construction of fully-diverse signal sets that lead to four-group encodable and
four-group decodable differential scaled unitary STBCs for any power of two
number of antennas is provided. Previous works on differential STBCs either
sacrifice decoding complexity for higher rate or sacrifice rate for lower
decoding complexity.Comment: 5 pages, 2 figures. To appear in Proceedings of IEEE ISIT 2007, Nice,
Franc

### OFDM based Distributed Space Time Coding for Asynchronous Relay Networks

Recently Li and Xia have proposed a transmission scheme for wireless relay
networks based on the Alamouti space time code and orthogonal frequency
division multiplexing to combat the effect of timing errors at the relay nodes.
This transmission scheme is amazingly simple and achieves a diversity order of
two for any number of relays. Motivated by its simplicity, this scheme is
extended to a more general transmission scheme that can achieve full
cooperative diversity for any number of relays. The conditions on the
distributed space time block code (DSTBC) structure that admit its application
in the proposed transmission scheme are identified and it is pointed out that
the recently proposed full diversity four group decodable DSTBCs from precoded
co-ordinate interleaved orthogonal designs and extended Clifford algebras
satisfy these conditions. It is then shown how differential encoding at the
source can be combined with the proposed transmission scheme to arrive at a new
transmission scheme that can achieve full cooperative diversity in asynchronous
wireless relay networks with no channel information and also no timing error
knowledge at the destination node. Finally, four group decodable distributed
differential space time block codes applicable in this new transmission scheme
for power of two number of relays are also provided.Comment: 5 pages, 2 figures, to appear in IEEE International Conference on
Communications, Beijing, China, May 19-23, 200

### Algebraic Distributed Differential Space-Time Codes with Low Decoding Complexity

The differential encoding/decoding setup introduced by Kiran et al,
Oggier-Hassibi and Jing-Jafarkhani for wireless relay networks that use
codebooks consisting of unitary matrices is extended to allow codebooks
consisting of scaled unitary matrices. For such codebooks to be usable in the
Jing-Hassibi protocol for cooperative diversity, the conditions involving the
relay matrices and the codebook that need to be satisfied are identified. Using
the algebraic framework of extended Clifford algebras, a new class of
Distributed Differential Space-Time Codes satisfying these conditions for power
of two number of relays and also achieving full cooperative diversity with a
low complexity sub-optimal receiver is proposed. Simulation results indicate
that the proposed codes outperform both the cyclic codes as well as the
circulant codes. Furthermore, these codes can also be applied as Differential
Space-Time codes for non-coherent communication in classical point to point
multiple antenna systems.Comment: To appear in IEEE Transactions on Wireless Communications. 10 pages,
5 figure

### A Relation Between Network Computation and Functional Index Coding Problems

In contrast to the network coding problem wherein the sinks in a network
demand subsets of the source messages, in a network computation problem the
sinks demand functions of the source messages. Similarly, in the functional
index coding problem, the side information and demands of the clients include
disjoint sets of functions of the information messages held by the transmitter
instead of disjoint subsets of the messages, as is the case in the conventional
index coding problem. It is known that any network coding problem can be
transformed into an index coding problem and vice versa. In this work, we
establish a similar relationship between network computation problems and a
class of functional index coding problems, viz., those in which only the
demands of the clients include functions of messages. We show that any network
computation problem can be converted into a functional index coding problem
wherein some clients demand functions of messages and vice versa. We prove that
a solution for a network computation problem exists if and only if a functional
index code (of a specific length determined by the network computation problem)
for a suitably constructed functional index coding problem exists. And, that a
functional index coding problem admits a solution of a specified length if and
only if a suitably constructed network computation problem admits a solution.Comment: 3 figures, 7 tables and 9 page

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