We identify three isotopic tracers that can be used to constrain the $^{13}C$-pocket and show the correlated isotopic ratios of Sr and Ba in single mainstream presolar SiC grains. These newly measured data can be explained by postprocess AGB model ca
lculations with large $^{13}C$-pockets with a range of relatively low $^{13}C$ concentrations, which may suggest that multiple mixing processes contributed to the $^{13}C$-pocket formation in parent AGB stars.
We present strontium, barium, carbon, and silicon isotopic compositions of 61 acid-cleaned presolar SiC grains from Murchison. Comparison with previous data shows that acid washing is highly effective in removing both strontium and barium contaminati
on. For the first time, by using correlated $^{88}Sr$/$^{86}Sr$ and $^{138}Ba$/$^{136}Ba$ ratios in mainstream SiC grains, we are able to resolve the effect of $^{13}C$ concentration from that of $^{13}C$-pocket mass on s-process nucleosynthesis, which points towards the existence of large $^{13}C$-pockets with low $^{13}C$ concentration in AGB stars. The presence of such large $^{13}$R-pockets with a variety of relatively low $^{13}C$ concentrations seems to require multiple mixing processes in parent AGB stars of mainstream SiC grains.
We present postprocess AGB nucleosynthesis models with different $^{13}$C-pocket internal structures to better explain zirconium isotope measurements in mainstream presolar SiC grains by Nicolussi et al. (1997) and Barzyk et al. (2007). We show that
higher-than-solar $^{92}$Zr/$^{94}$Zr ratios can be predicted by adopting a $^{13}$C-pocket with a flat $^{13}$C profile, instead of the previous decreasing-with-depth $^{13}$C profile. The improved agreement between grain data for zirconium isotopes and AGB models provides additional support for a recent proposal of a flat $^{13}$C profile based on barium isotopes in mainstream SiC grains by Liu et al. (2014).
We study the discrete memoryless Z-interference channel (ZIC) where the transmitter of the pair that suffers from interference is cognitive. We first provide upper and lower bounds on the capacity of this channel. We then show that, when the channel
of the transmitter-receiver pair that does not face interference is noiseless, the two bounds coincide and therefore yield the capacity region. The obtained results imply that, unlike in the Gaussian cognitive ZIC, in the considered channel superposition encoding at the non-cognitive transmitter as well as Gelfand-Pinsker encoding at the cognitive transmitter are needed in order to minimize the impact of interference. As a byproduct of the obtained capacity region, we obtain the capacity result for a generalized Gelfand-Pinsker problem.
The problem of joint source-channel coding in transmitting independent sources over interference channels with correlated receiver side information is studied. When each receiver has side information correlated with its own desired source, it is show
n that source-channel code separation is optimal. When each receiver has side information correlated with the interfering source, sufficient conditions for reliable transmission are provided based on a joint source-channel coding scheme using the superposition encoding and partial decoding idea of Han and Kobayashi. When the receiver side information is a deterministic function of the interfering source, source-channel code separation is again shown to be optimal. As a special case, for a class of Z-interference channels, when the side information of the receiver facing interference is a deterministic function of the interfering source, necessary and sufficient conditions for reliable transmission are provided in the form of single letter expressions. As a byproduct of these joint source-channel coding results, the capacity region of a class of Z-channels with degraded message sets is also provided.
