A New Scheme to Identify Good Codes for OFDM with Low PMEPR

Golay complementary sequences have been introduced to encode the orthogonal frequency division multiplexing (OFDM) signals. In this paper, we extend Golay complementary sequences to sub-root sequences. Based on sub-root sequences, we propose a new scheme to construct good codes for OFDM with low PMEPR, which has the potential to discover Golay-Davis-Jedwab (GDJ), non-GDJ complementary codes and non-complementary codes. We firstly build the main construction theorem. Then we build short length root codes represented by Boolean functions ℤ2m → ℤM, which are not the form of GDJ complementary sequences, but with low PMEPR. By our theorem, we then extend them to long length root codes with the same PMEPR. In this way, we offer an efficient method to identify a large number of codes for OFDM with low PMEPR.