We consider joint source-channel and multiuser decoding for frequency-selec
tive Rayleigh fading code-division multiple-access channels. The block sour
ce-channel encoder is defined by a vector quantizer, We investigate optimal
(minimum mean-square error) decoding and "user-separated" decoding of lowe
r complexity, The studied decoders are soft in the sense that they utilize
all soft information available at the receiver. Simulations indicate signif
icant performance gains of the introduced decoders compared with a tandem a
pproach that uses maximum-likelihood multiuser detection plus table-lookup
decoding.