Unfortunately, sleeping anywhere - bed, sofa, floor - with the infant nearby is not recommended.
From the CDC site:
Have the baby share your room, not your bed. Your baby should not sleep in an adult bed, on a couch, or on a chair alone, with you, or with anyone else.
From the AAP:
The AAP recommends the arrangement of room-sharing without bed-sharing, or having the infant sleep in the parents' room but on a separate sleep surface (crib or similar surface) close to [but not attached to] the parents' bed.
Evidence exists that room sharing without bed sharing decreases the risk of SIDS by as much as 50%, is safer than bed-sharing, or solitary sleeping (in a separate room). In addition, this arrangement is most likely to prevent suffocation, etc., which may occur when the infant is sleeping in the adult bed. Room-sharing without bed-sharing gives the parents close proximity making feeding, comforting, and monitoring of the infant easier.
In a study from Scotland focusing on sharing sleep surfaces, of 123 infants who dies of SIDS between May 1996 and Jan 2000, the highest risk was associated with couch-sharing, then bedsharing. The final recommendation was against bed-sharing for infants <11 weeks of age, and sharing a couch for sleep should be strongly discouraged at any age.
In this article promoting safe bedsharing, the author implies that bedsharing decreased SIDS because breastfeeding reduces SIDS, and bedsharing promotes breastfeeding. The fact is that parents get better sleep if they don't have to get up to breastfeed, which is the factor promoting breastfeeding. The benefit of breastfeeding in the reduction of SIDS is independent of sleep surfaces.
I would love to say sharing a bed is fine and good. But I can't, not yet. I successfully breastfed my children without bedsharing, so I know it's possible.
SIDS and Other Sleep-Related Infant Deaths: Expansion of Recommendations for a Safe Infant Sleeping Environment: Task Force on Sudden Infant Death Syndrome
Bedsharing, roomsharing, and sudden infant death syndrome in Scotland: a case-control study