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18
Spacetime codes for high data rate wireless communication: Performance criterion and code construction
 IEEE TRANS. INFORM. THEORY
, 1998
"... We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit ant ..."
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Cited by 1568 (27 self)
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We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. We derive performance criteria for designing such codes under the assumption that the fading is slow and frequency nonselective. Performance is shown to be determined by matrices constructed from pairs of distinct code sequences. The minimum rank among these matrices quantifies the diversity gain, while the minimum determinant of these matrices quantifies the coding gain. The results are then extended to fast fading channels. The design criteria are used to design trellis codes for high data rate wireless communication. The encoding/decoding complexity of these codes is comparable to trellis codes employed in practice over Gaussian channels. The codes constructed here provide the best tradeoff between data rate, diversity advantage, and trellis complexity. Simulation results are provided for 4 and 8 PSK signal sets with data rates of 2 and 3 bits/symbol, demonstrating excellent performance that is within 2–3 dB of the outage capacity for these channels using only 64 state encoders.
On the trellis structure of block codes
 in Proc. 32nd Annual Allerton Con$ on Communication, Control, and Computing (Allerton, IL
, 1995
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Algorithmic Complexity in Coding Theory and the Minimum Distance Problem
, 1997
"... We start with an overview of algorithmiccomplexity problems in coding theory We then show that the problem of computing the minimum distance of a binary linear code is NPhard, and the corresponding decision problem is NPcomplete. This constitutes a proof of the conjecture Bedekamp, McEliece, van T ..."
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Cited by 36 (2 self)
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We start with an overview of algorithmiccomplexity problems in coding theory We then show that the problem of computing the minimum distance of a binary linear code is NPhard, and the corresponding decision problem is NPcomplete. This constitutes a proof of the conjecture Bedekamp, McEliece, van Tilborg, dating back to 1978. Extensions and applications of this result to other problems in coding theory are discussed.
SoftDecision Decoding of ReedMuller Codes as Generalized Multiple Concatenated Codes
 IEEE Trans. Inform. Theory
, 1995
"... In this paper, we present a new softdecision decoding algorithm for ReedMuller codes. It is based on the GMC decoding algorithm proposed by Schnabl and Bossert [1] which interprets ReedMuller codes as generalized multiple concatenated codes. We extend the GMC algorithm to listdecoding (LGMC). A ..."
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Cited by 16 (1 self)
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In this paper, we present a new softdecision decoding algorithm for ReedMuller codes. It is based on the GMC decoding algorithm proposed by Schnabl and Bossert [1] which interprets ReedMuller codes as generalized multiple concatenated codes. We extend the GMC algorithm to listdecoding (LGMC). As a result, a SDML decoding algorithm for the first order ReedMuller codes is obtained. Moreover, the performance achieved with LGMC for ReedMuller codes of higher order is considerably better compared to GMC. In particular, for the ReedMuller codes of length ¢¡¤ £ , quasi SDML decoding performance is obtained at a computational complexity that is by far less than optimum decoding using the syndrome trellis [2]. Simulations will also show that for ReedMuller codes up to a length 1024, the performance of LGMC decoding is more than 1dB superior to conventional GMC decoding. 1
The trellis complexity of convolutional codes
 IEEE Trans. Inform. Theory
, 1996
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Computational Methods in Coding Theory
, 1996
"... We consider various computational techniques in algebraic coding theory along two lines of work. First we investigate optimization of nonlinear codes by relaxing minimum distance constraints, developing, in the process, two algorithms for improving a given nonlinear code and a method of visualizin ..."
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Cited by 3 (1 self)
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We consider various computational techniques in algebraic coding theory along two lines of work. First we investigate optimization of nonlinear codes by relaxing minimum distance constraints, developing, in the process, two algorithms for improving a given nonlinear code and a method of visualizing algebraic codes in three dimensions. Secondly, we study the Generalized Lexicographic Construction, and show that it produces as special cases the lexicodes and derivatives with properties such as trellisorientation, trellisstate boundedness, and local optimality. We implement algorithms for generating these families of codes and, in the process, improve upon work by Conway and Sloane, Brualdi and Pless, Kschischang and Horn, and Zhang.
Good trellises for IC implementation of Viterbi decoders for linear block codes
 IEEE Trans. Communications
, 1997
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Ordered Binary Decision Diagrams and Minimal Trellises
 IEEE Transactions on Computers
, 1999
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Good Trellises for IC Implementation of Viterbi
, 1996
"... This paper investigates trellis structures of linear block codes for the IC (integrated circuit) implementation of Viterbi decoders capable of achieving high decoding speed while satisfying a constraint on the structural complexity of the trellis in terms of the maximum number of states at any parti ..."
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This paper investigates trellis structures of linear block codes for the IC (integrated circuit) implementation of Viterbi decoders capable of achieving high decoding speed while satisfying a constraint on the structural complexity of the trellis in terms of the maximum number of states at any particular depth. Only uniform sectionalizations of the code trellis diagram are considered. An upper bound on the number of parallel and structurally identical (or isomorphic) subtrellises in a proper trellis for a code without exceeding the maximum state complexity of the minimal trellis of the code is first derived. Parallel structures of trellises with various section lengths for binary BCH and ReedMuller (RM) codes of lengths:.12 and 64 are analyzed. Next, the complexity of IC implementation of a Viterbi decoder based on an Lsection trellis diagram for a code is investigated. A structural property of a Viterbi decoder called ACSconnectivity which is related to state connectivity is introduced. This parameter affects the complexity of wirerouting (interconnections within the IC). The effect of five parameters namely: (1) effective computational complexity; (2) complexity of the ACScircuit; (3) traceback complexity; (4) ACSconnectivity; and (5)
Introducton to the Special Issue on Codes and Complexity
, 1996
"... This paper continues the work of Lafourcade and Vardy [18], tabulated on ..."