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Title:  HighRate And InformationLossless SpaceTime Block Codes From CrossedProduct Algebras 
Authors:  Shashidhar, V 
Advisors:  SundarRajan, B 
Keywords:  Antennas Signal Processing  Digital Techniques AsymptoticInformationLossless (AILL) Designs CrossedProduct Algebras SpaceTime Block Codes (STBC) Orthogonal Designs Quasiorthogonal Designs Algebra DiversityMultiplexing Tradeoff SpaceTime Coding (STC) 
Submitted Date:  Apr2004 
Abstract:  It is well known that communication systems employing multiple transmit and multiple receive antennas provide high data rates along with increased reliability. It has been shown that coding across both spatial and temporal domains together, called SpaceTime Coding (STC), achieves, a diversity order equal to the product of the number of transmit and receive antennas. SpaceTime Block Codes (STBC) achieving the maximum diversity is called fulldiversity STBCs. An STBC is called informationlossless, if the structure of it is such that the maximum mutual information of the resulting equivalent channel is equal to the capacity of the channel.
This thesis deals with highrate and informationlossless STBCs obtained from certain matrix algebras called CrossedProduct Algebras. First we give constructions of highrate STBCs using both commutative and noncommutative matrix algebras obtained from appropriate representations of extensions of the field of rational numbers. In the case of commutative algebras, we restrict ourselves to fields and call the STBCs obtained from them as STBCs from field extensions. In the case of noncommutative algebras, we consider only the class of crossedproduct algebras.
For the case of field extensions, we first construct highrate; fulldiversity STBCs for arbitrary number of transmit antennas, over arbitrary apriori specified signal sets. Then we obtain a closed form expression for the coding gain of these STBCs and give a tight lower bound on the coding gain of some of these STBCs. This lower bound in certain cases indicates that some of the STBCs from field extensions are optimal m the sense of coding gain. We then show that the STBCs from field extensions are informationlossy. However, we also show that the finitesignalset capacity of the STBCs from field extensions can be improved by increasing the symbol rate of the STBCs. The simulation results presented show that our highrate STBCs perform better than the rate1 STBCs in terms of the bit error rate performance.
Then we proceed to present a construction of highrate STBCs from crossedproduct algebras. After giving a sufficient condition on the crossedproduct algebras under which the resulting STBCs are informationlossless, we identify few classes of crossedproduct algebras that satisfy this sufficient condition and also some classes of crossedproduct algebras which are division algebras which lead to fulldiversity STBCs. We present simulation results to show that the STBCs from crossedproduct algebras perform better than the wellknown codes m terms of the bit error rate.
Finally, we introduce the notion of asymptoticinformationlossless (AILL) designs and give a necessary and sufficient condition under which a linear design is an AILL design. Analogous to the condition that a design has to be a fullrank design to achieve the point corresponding to the maximum diversity of the optimal diversitymultiplexing tradeoff, we show that a design has to be AILL to achieve the point corresponding to the maximum multiplexing gain of the optimal diversitymultiplexing tradeoff. Using the notion of AILL designs, we give a lower bound on the diversitymultiplexing tradeoff achieved by the STBCs from both field extensions and division algebras. The lower bound for STBCs obtained from division algebras indicates that they achieve the two extreme points, 1 e, zero multiplexing gain and zero diversity gain, of the optimal diversitymultiplexing tradeoff. Also, we show by simulation results that STBCs from division algebras achieves all the points on the optimal diversitymultiplexing tradeoff for n transmit and n receive antennas, where n = 2, 3, 4. 
URI:  http://hdl.handle.net/2005/314 
Appears in Collections:  Electrical Communication Engineering (ece)

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