Generalized upper bounds on the minimum distance of PSK block codes

This paper generalizes previous optimal upper bounds on the minimum Euclidean distance for phase shift keying (PSK) block codes, that are explicit in three parameters: alphabet size, block length and code size. The bounds are primarily generalized from codes over symmetric PSK to codes over asymmetric PSK and also to general alphabet size. Furthermore, block codes are optimized in the presence of other types of noise than Gaussian, which induces also non-Euclidean distance measures. In some instances, codes over asymmetric PSK prove to give higher Euclidean distance than any code over symmetric PSK with the same parameters. We also provide certain classes of codes that are optimal among codes over symmetric PSK.Detta papper generaliserar tidigare optimala övre gränser för minimala Euklidiska avståndet för fasskift block koder, s.k. phase shift keying (PSK). De är explicita i tre parametrar: alfabetstorlek, blocklängd och kodstorlek. Gränserna är framförallt generaliserade från koder över symmetrisk PSK till koder över asymmetrisk PSK men även till generell alfabetsstorlek. Block koder är även generaliserade i närvaro av annat brus än gaussiskt, vilket leder till icke-Euklidiska avståndsmått. I vissa fall ger asymmetrisk PSK högre Euklidiskt avstånd än symmetriskt med samma parametrar. Vi visar också att vissa kodklasser är optimala i gruppen av symmetrisk PSK.Open access article</p

In press: Generalized upper bounds on the minimum distance of PSK block codes

This paper generalizes previous optimal upper bounds on the minimum Euclidean distance for phase shift keying (PSK) block codes, that are explicit in three parameters: alphabet size, block length and code size. The bounds are primarily generalized from codes over symmetric PSK to codes over asymmetric PSK and also to general alphabet size. Furthermore, block codes are optimized in the presence of other types of noise than Gaussian, which induces also non-Euclidean distance measures. In some instances, codes over asymmetric PSK prove to give higher Euclidean distance than any code over symmetric PSK with the same parameters. We also provide certain classes of codes that are optimal among codes over symmetric PSK