Switchable-rate quasi-cyclic low-density parity-check codes for internet protocol over high-frequency systems

Complementary M ‐ary orthogonal spreading OFDM architecture for HF communication link

“…Proof: After the first iteration from C (0) , aperiodic ACF and CCF between adjacent sequences of S (1) are, respectively, calculated as…”

“…From (11) and 12, by combining ideal aperiodic ACF and CCF of C (0) with orthogonality of E in (9), we may obtain that each pair of S (1) has ideal aperiodic ACF and any two adjacent complementary pairs of S (1) m,0 ; S (1) m,1 and S (1) m+1,0 ; S (1) m+1,1 with even m have ideal aperiodic CCF.…”

“…For orthogonality of S (1) , it may be easily obtained on the basis of ideal correlation property of C (0) and orthogonality of E, and is omitted. After the nth iteration, the aperiodic ACF, aperiodic CCF and orthogonality of S (n) can be similarly obtained.…”

“…High frequency (HF) communications, usually from 1.5 to 30 MHz, play important roles in long-range transmission and worldwide coverage, since HF radio waves are capable of travelling well beyond line of sight by means of reflections from the ionosphere. As a powerful complementary or alternative technology to satellite communications, HF communication may possess lower cost and larger flexibility [1]. However, communications in HF band are not considered to be reliable, due to large variations and highly dispersive characteristics of the HF channel, such as multi-path delay, Doppler spread, noise and interferences [2][3][4].…”