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

Abstract

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.

Near-Complementary Sequences With Low PMEPR for Peak Power Control in Multicarrier Communications

“…It implies that the code rate loss induced by choosing distinct sequences is negligible for m ≥ 5, and we are able to obtain a sufficiently large number of distinct sequences from Construction 2. Also, we observed that the code rate R dist for a given m is higher than the ones in any other known near-complementary sequences [15][16] [20].…”

“…When t = 0, we realize that the near-complementary sequences from Construction 2 are equivalent to the codewords in Golay complementary sets of size 4 and PMEPR ≤ 4 from Construction 14 in [20]. In the paper, the author indicated the potential of applying a permutation to the m variables in the Boolean function for increasing the number of codewords.…”

“…Moreover, we developed a generation algorithm of permutations for the sequences at t = 1. As a result, our sequence family contains the codewords from Construction 14 in [20] as its subset. The more sequences in the family enables the higher code rates than in [20].…”

“…As a result, our sequence family contains the codewords from Construction 14 in [20] as its subset. The more sequences in the family enables the higher code rates than in [20]. 20 …”

“…For further researches on Golay complementary sets and near-complementary sequences, see [5][15] [20].…”