A light-emitting system includes a first and second power input terminals; a first, second, third, and fourth light-emitting-diode groups each having at least one light-emitting diode; a first circuit path having at least one diode from each of the first and second light-emitting-diode groups, with the diodes coupled serially and emitting light during a positive power cycle; and a second circuit path having at least one diode from each of the third and fourth light-emitting-diode groups, with the diodes coupled serially and emitting light during a negative power cycle. The second light-emitting-diode group and the third light-emitting-diode group share at least one common diode, The first and second power input terminals, the first, second, third, and fourth light-emitting-diode groups, and the first and second circuit paths may belong to a single chip light-emitting system.