Construction of complementary code sequence sets, part 7.1D

A set of code sequences is a complementary code sequence set if the sum of the aperiodic autocorrelation functions for the sequences is zero everywhere except at the origin. A simple construction for sets of complementary code sequences is discussed

Generalized pairwise z-complementary codes

An approach to generate generalized pairwise Z-complementary (GPZ) codes, which works in pairs in order to offer a zero correlation zone (ZCZ) in the vicinity of zero phase shift and fit extremely well in power efficient quadrature carrier modems, is introduced in this letter. Each GPZ code has MK sequences, each of length 4NK, whereMis the number of Z-complementary mates, K is a factor to perform Walsh–Hadamard expansions, and N is the sequence length of the Z-complementary code. The proposed GPZ codes include the generalized pairwise complementary (GPC)codes as special cases

Autocorrelations of Binary Sequences and Run Structure

We analyze the connection between the autocorrelation of a binary sequence and its run structure given by the run length encoding. We show that both the periodic and the aperiodic autocorrelation of a binary sequence can be formulated in terms of the run structure. The run structure is given by the consecutive runs of the sequence. Let C=(C(0), C(1),...,C(n)) denote the autocorrelation vector of a binary sequence. We prove that the kth component of the second order difference operator of C can be directly calculated by using the consecutive runs of total length k. In particular this shows that the kth autocorrelation is already determined by all consecutive runs of total length L<k. In the aperiodic case we show how the run vector R can be efficiently calculated and give a characterization of skew-symmetric sequences in terms of their run length encoding.Comment: [v3]: minor revisions, accepted for publication in IEEE Trans. Inf. Theory, 17 page

Complementary Sets, Generalized Reed-Muller Codes, and Power Control for OFDM

The use of error-correcting codes for tight control of the peak-to-mean envelope power ratio (PMEPR) in orthogonal frequency-division multiplexing (OFDM) transmission is considered in this correspondence. By generalizing a result by Paterson, it is shown that each q-phase (q is even) sequence of length 2^m lies in a complementary set of size 2^{k+1}, where k is a nonnegative integer that can be easily determined from the generalized Boolean function associated with the sequence. For small k this result provides a reasonably tight bound for the PMEPR of q-phase sequences of length 2^m. A new 2^h-ary generalization of the classical Reed-Muller code is then used together with the result on complementary sets to derive flexible OFDM coding schemes with low PMEPR. These codes include the codes developed by Davis and Jedwab as a special case. In certain situations the codes in the present correspondence are similar to Paterson's code constructions and often outperform them