34 research outputs found
Distributed space-time block codes for two-hop wireless relay networks
Recently, the idea of space-time coding has been applied to wireless relay networks wherein a set of geographically separated relay nodes cooperate to process the received signal from the source and forward them to the destination such that the signal received at the destination appears like a Space-Time Block Code (STBC). Such STBCs (referred to as Distributed Space-Time Block Codes (DSTBCs)) when appropriately designed are known to offer spatial diversity. It is known that different classes of DSTBCs can be designed primarily depending on (i) whether the Amplify and Forward (AF) protocol or the Decode and Forward (DF) protocol is employed at the relays and (ii) whether the relay nodes are synchronized or not. In this paper, we present a survey on the problems and results associated with the design of DSTBCs for the following classes of two-hop wireless relay networks: (i) synchronous relay networks with AF protocols, (ii) asynchronous relay networks with AF protocols (iii) synchronous relay networks with DF protocols and (iv) asynchronous relay Fig. 1. Co-located MIMO channel model networks with DF protocols
STBCs from Representation of Extended Clifford Algebras
A set of sufficient conditions to construct -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 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
New Soft Set Based Class of Linear Algebraic Codes
In this paper, we design and develop a new class of linear algebraic codes defined as soft linear algebraic codes using soft sets. The advantage of using these codes is that they have the ability to transmit m-distinct messages to m-set of receivers simultaneously. The methods of generating and decoding these new classes of soft linear algebraic codes have been developed. The notion of soft canonical generator matrix, soft canonical parity check matrix, and soft syndrome are defined to aid in construction and decoding of these codes. Error detection and correction of these codes are developed and illustrated by an example
High Rate Single-Symbol Decodable Precoded DSTBCs for Cooperative Networks
Distributed Orthogonal Space-Time Block Codes (DOSTBCs) achieving full
diversity order and single-symbol ML decodability have been introduced recently
for cooperative networks and an upper-bound on the maximal rate of such codes
along with code constructions has been presented. In this report, we introduce
a new class of Distributed STBCs called Semi-orthogonal Precoded Distributed
Single-Symbol Decodable STBCs (S-PDSSDC) wherein, the source performs
co-ordinate interleaving of information symbols appropriately before
transmitting it to all the relays. It is shown that DOSTBCs are a special case
of S-PDSSDCs. A special class of S-PDSSDCs having diagonal covariance matrix at
the destination is studied and an upper bound on the maximal rate of such codes
is derived. The bounds obtained are approximately twice larger than that of the
DOSTBCs. A systematic construction of S-PDSSDCs is presented when the number of
relays . The constructed codes are shown to achieve the upper-bound
on the rate when is of the form 0 modulo 4 or 3 modulo 4. For the rest of
the values of , the constructed codes are shown to have rates higher than
that of DOSTBCs. It is also shown that S-PDSSDCs cannot be constructed with any
form of linear processing at the relays when the source doesn't perform
co-ordinate interleaving of the information symbols.Comment: A technical report of DRDO-IISc Programme on Advanced Research in
Mathematical Engineerin
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
Finite-Block-Length Analysis in Classical and Quantum Information Theory
Coding technology is used in several information processing tasks. In
particular, when noise during transmission disturbs communications, coding
technology is employed to protect the information. However, there are two types
of coding technology: coding in classical information theory and coding in
quantum information theory. Although the physical media used to transmit
information ultimately obey quantum mechanics, we need to choose the type of
coding depending on the kind of information device, classical or quantum, that
is being used. In both branches of information theory, there are many elegant
theoretical results under the ideal assumption that an infinitely large system
is available. In a realistic situation, we need to account for finite size
effects. The present paper reviews finite size effects in classical and quantum
information theory with respect to various topics, including applied aspects