Variable-length coding for mixed sources with side information allowing decoding errors

Variable-length source coding with side information allowing a nonzero decoding error probability ε is considered. For the case where the side information is available at both of the encoder and decoder, we give an explicit formula of the rate-error function R
_c
(ε) for the mixture of i.i.d. sources. For the case where the side information is available only at the decoder, we concentrate our attention on the mixture of binary symmetric sources. Our result gives a simple way to draw the graph of the rate-error function R(ε).