Short Packets over Block-Memoryless Fading Channels: Pilot-Assisted or Noncoherent Transmission?

We present nonasymptotic upper and lower bounds on the maximum coding rate achievable when transmitting short packets over a Rician memoryless block-fading channel for a given requirement on the packet error probability. We focus on the practically relevant scenario in which there is no \emph{a priori} channel state information available at the transmitter and at the receiver. An upper bound built upon the min-max converse is compared to two lower bounds: the first one relies on a noncoherent transmission strategy in which the fading channel is not estimated explicitly at the receiver; the second one employs pilot-assisted transmission (PAT) followed by maximum-likelihood channel estimation and scaled mismatched nearest-neighbor decoding at the receiver. Our bounds are tight enough to unveil the optimum number of diversity branches that a packet should span so that the energy per bit required to achieve a target packet error probability is minimized, for a given constraint on the code rate and the packet size. Furthermore, the bounds reveal that noncoherent transmission is more energy efficient than PAT, even when the number of pilot symbols and their power is optimized. For example, for the case when a coded packet of $168$ symbols is transmitted using a channel code of rate $0.48$ bits/channel use, over a block-fading channel with block size equal to $8$ symbols, PAT requires an additional $1.2$ dB of energy per information bit to achieve a packet error probability of $10^{-3}$ compared to a suitably designed noncoherent transmission scheme. Finally, we devise a PAT scheme based on punctured tail-biting quasi-cyclic codes and ordered statistics decoding, whose performance are close ($1$ dB gap at $10^{-3}$ packet error probability) to the ones predicted by our PAT lower bound. This shows that the PAT lower bound provides useful guidelines on the design of actual PAT schemes.Comment: 30 pages, 5 figures, journa

Indirect Reference Intervals Estimated from Hospitalized Population for Thyrotropin and Free Thyroxine

Aim To establish indirect reference intervals from patient results obtained during routine laboratory work as an alternative to laborious and expensive producing of their own reference range values according to international instructions. Methods All results for thyrotropin (TSH) and free thyroxine (T4) that were stored in our laboratory information system between 2004 and 2008 were included in this study. After a logarithmic transformation of the raw data, outliers were excluded. Non-parametric reference intervals were estimated statistically after visual observation of the distribution using stem-and-leaf plots and histograms. A standard normal deviation test was performed to test the significance of differences between sub-groups. Results There was no significant difference in serum TSH or free T4 concentrations between male and female participants. Because no differences were found within the time span of the study, combined reference intervals were calculated. Indirect reference values were 0.43-3.93 mU/L for TSH and 11.98-21.33 pmol/L for free T4. Conclusion Using patient laboratory data values is a relatively easy and cheap method of establishing laboratoryspecific reference values if skewness and kurtosis of the distribution are not too large

Indirect Reference Intervals Estimated from Hospitalized Population for Thyrotropin and Free Thyroxine

Aim To establish indirect reference intervals from patient results obtained during routine laboratory work as an alternative to laborious and expensive producing of their own reference range values according to international instructions. Methods All results for thyrotropin (TSH) and free thyroxine (T4) that were stored in our laboratory information system between 2004 and 2008 were included in this study. After a logarithmic transformation of the raw data, outliers were excluded. Non-parametric reference intervals were estimated statistically after visual observation of the distribution using stem-and-leaf plots and histograms. A standard normal deviation test was performed to test the significance of differences between sub-groups. Results There was no significant difference in serum TSH or free T4 concentrations between male and female participants. Because no differences were found within the time span of the study, combined reference intervals were calculated. Indirect reference values were 0.43-3.93 mU/L for TSH and 11.98-21.33 pmol/L for free T4. Conclusion Using patient laboratory data values is a relatively easy and cheap method of establishing laboratoryspecific reference values if skewness and kurtosis of the distribution are not too large