On Spectrally-Bounded Codes for Multicarrier Communications
1st Edition
Published on 4. June 2007
Book
VIII, 164 pages
978-3-938860-07-6 (ISBN)
Description
In multicarrier communications the transmitted signal is obtained by applying an orthogonal transform to a block of data symbols. As a consequence, the peak power of the transmitted signal can be much larger than its mean power, which makes the practical implementation of the system a challenging task.
The redundancy of carefully designed error-correcting codes can be exploited to control the ratio of the peak and the mean power of the transmitted signal. In this thesis such codes are studied for two types of multicarrier communications systems: orthogonal frequency-division multiplexing (OFDM) and multicode code-division multiple access (MC-CDMA).
In a first part of this thesis a well-known approach for the construction of such codes for OFDM is examined. This concept involves a rotation of the coordinates of a known binary code by phase shifts that are independent of the individual codewords. Bounds for the maximum reduction of the peak-to-mean power ratio are proved, and it is shown that most phase-shift designs in the literature, obtained using suboptimal optimization methods, produce peak-to-mean power ratio reductions that are close to the theoretical limit.
The spectral properties of complementary pairs and generalizations, namely near-complementary pairs and complementary sets, are then exploited to prove upper and lower bounds on the peak-to-mean power ratio of certain cosets of a first-order generalized Reed-Muller code. By taking unions of such cosets inside higher-order generalized Reed-Muller codes, error-correcting codes for OFDM and MC-CDMA with strictly bounded peak-to-mean power ratios are constructed. These codes complement and, in many situations, improve existing coding schemes.
Moreover these results provide theoretical support for conjectures and empirical observations in the literature. Finally generalized bent functions in connection with algebraic codes over Z4, namely generalized Reed-Muller, Kerdock, and Delsarte-Goethals codes, are exploited to construct families of so-called constant-amplitude error-correcting codes for MC-CDMA, which are codes that reduce the peak-to-mean power ratio to the least possible value. These codes complement previously proposed binary constant-amplitude codes.
The redundancy of carefully designed error-correcting codes can be exploited to control the ratio of the peak and the mean power of the transmitted signal. In this thesis such codes are studied for two types of multicarrier communications systems: orthogonal frequency-division multiplexing (OFDM) and multicode code-division multiple access (MC-CDMA).
In a first part of this thesis a well-known approach for the construction of such codes for OFDM is examined. This concept involves a rotation of the coordinates of a known binary code by phase shifts that are independent of the individual codewords. Bounds for the maximum reduction of the peak-to-mean power ratio are proved, and it is shown that most phase-shift designs in the literature, obtained using suboptimal optimization methods, produce peak-to-mean power ratio reductions that are close to the theoretical limit.
The spectral properties of complementary pairs and generalizations, namely near-complementary pairs and complementary sets, are then exploited to prove upper and lower bounds on the peak-to-mean power ratio of certain cosets of a first-order generalized Reed-Muller code. By taking unions of such cosets inside higher-order generalized Reed-Muller codes, error-correcting codes for OFDM and MC-CDMA with strictly bounded peak-to-mean power ratios are constructed. These codes complement and, in many situations, improve existing coding schemes.
Moreover these results provide theoretical support for conjectures and empirical observations in the literature. Finally generalized bent functions in connection with algebraic codes over Z4, namely generalized Reed-Muller, Kerdock, and Delsarte-Goethals codes, are exploited to construct families of so-called constant-amplitude error-correcting codes for MC-CDMA, which are codes that reduce the peak-to-mean power ratio to the least possible value. These codes complement previously proposed binary constant-amplitude codes.