Writing on Fading Paper and Causal Transmitter CSI

A wideband fading channel is considered with causal channel state information (CSI) at the transmitter and no receiver CSI. A simple orthogonal code with energy detection rule at the receiver (similar to [6]) is shown to achieve the capacity of this channel in the limit of large bandwidth. This code transmits energy only when the channel gain is large enough. In this limit, this capacity without any receiver CSI is the same as the capacity with full receiver CSI--a phenomenon also true for dirty paper coding. For Rayleigh fading, this capacity (per unit time) is proportional to the logarithm of the bandwidth. Our coding scheme is motivated from the Gel'fand-Pinsker [2,3] coding and dirty paper coding [4]. Nonetheless, for our case, only causal CSI is required at the transmitter in contrast with dirty-paper coding and Gel'fand-Pinsker coding, where non-causal CSI is required. Then we consider a general discrete channel with i.i.d. states. Each input has an associated cost and a zero cost input "0" exists. The channel state is assumed be to be known at the transmitter in a causal manner. Capacity per unit cost is found for this channel and a simple orthogonal code is shown to achieve this capacity. Later, a novel orthogonal coding scheme is proposed for the case of causal transmitter CSI and a condition for equivalence of capacity per unit cost for causal and non-causal transmitter CSI is derived. Finally, some connections are made to the case of non-causal transmitter CSI in [8]

Wideband Fading Channels With Feedback

The Rayleigh flat fading channel at low SNR is considered. With full channel state information (CSI) at the transmitter and receiver, its capacity is shown to be essentially SNR log(1SNR) nats/symbol, as SNR goes to zero. In fact, this rate can be achieved with a just one bit of CSI at the transmitter (per fading realization) and with no receiver CSI. The capacity for the case of noisy transmitter CSI is also found. Then a Rayleigh block fading channel of coherence interval T ≤ 1/ SNR is considered which has causal feedback and no a priori CSI. A training based scheme is proposed for such channels, which achieves a rate of SNR logT nats/symbol in the limit of small SNR and large T. Thus, when coherence interval T is of the order 1/SNR, without any a priori CSI at either end, the capacity with full CSI at both ends is achievable. For smaller values of T, a rate of SNR logT nats/symbol is shown to be achievable

Writing on Fading Paper and Causal Transmitter CSI,” preprint at http://arxiv.org/PS cache/cs/pdf/0511/0511081.pdf

Abstract — 1 A wideband fading channel is considered with causal channel state information (CSI) at the transmitter and no receiver CSI. A simple orthogonal code with energy detection rule at the receiver is shown to achieve the capacity of this channel in the limit of large bandwidth. This code transmits energy only when the channel gain is large enough. In this limit, this capacity without any receiver CSI is the same as the capacity with full receiver CSI–a phenomenon also true for dirty paper coding. For Rayleigh fading, this capacity (per unit time) is proportional to the logarithm of the bandwidth. Our coding scheme is motivated from the Gel’fand-Pinsker and dirty paper coding. Nonetheless, our scheme requires only causal transmitter CSI (CSIT) in contrast with Gel’fand-Pinsker and dirty paper coding, which require non-causal CSIT. A general discrete channel with i.i.d. states is considered later. Each input has an associated cost and a zero cost input “0” exists. The channel state is known at the transmitter in a causal manner. Capacity per unit cost is found for this channel and a simple orthogonal code is shown to achieve it. Later, a novel orthogonal coding scheme is proposed for the case of causal CSIT and a condition for equal capacity per unit cost with causal and non-causal CSIT is derived. I

Multilevel Broadcast Networks

Abstract—We formulate a broadcast problem, where based on their quality of observations, outputs at various receivers are represented on a graph (called “degradation graph”). If receiver Z is a physically degraded version of receiver Y, then node Z is a child of node Y in this graph. This generalization of the classical degraded broadcast channel provides a framework for various situations where at least some information should be available to receivers with partial (or noisier) observations. Upper and lower bounds are obtained on the capacity region. The upper bound is based on auxiliary variables, whose structure is described by the mirror image of the channel’s degradation graph. As a special case of our problem, a packet broadcast network is considered. I

Unequal Error Protection: An Information-Theoretic Perspective

An information-theoretic framework for unequal error protection is developed in terms of the exponential error bounds. The fundamental difference between the bit-wise and message-wise unequal error protection ( UEP) is demonstrated, for fixed-length block codes on discrete memoryless channels (DMCs) without feedback. Effect of feedback is investigated via variable-length block codes. It is shown that, feedback results in a significant improvement in both bit-wise and message-wise UEPs (except the single message case for missed detection). The distinction between false-alarm and missed-detection formalizations for message-wise UEP is also considered. All results presented are at rates close to capacity.United States. Air Force Office of Scientific Research (Grant FA9550-06-0156)Defense Advanced Research Projects Agency, ITMANET projec

some fundamental limits of unequal error protection

An information theoretic framework for unequal error protection is developed in terms of the exponential error bounds. The fundamental difference between the bit-wise and message-wise unequal error protection (UEP ) is demonstrated, for fixed length block codes on DMCs without feedback. Effect of feedback is investigated via variable length block codes. It is shown that, feedback results in a significant improvement in both bit-wise and message-wise UEP (except the single message case for missed detection). The distinction between false-alarm and missed-detection formalizations for message-wise UEP is also considered. All results presented are at rates close to capacity

Growth status of children and adolescents with type 1 diabetes mellitus

Background and Objectives: Growth parameters are important indicators of a child′s overall health, and they are influenced by factors like blood glucose control in diabetic children. Data on growth parameters of Indian diabetic children is scarce. This retrospective, cross-sectional, case control study was conducted at diabetes clinic for children at a tertiary care center at Pune, to study growth parameters of diabetic children in comparison with age-gender matched healthy controls and evaluate effect of different insulin regimes and age at diagnosis of diabetes on growth. Materials and Methods: One twenty five diabetic children (boys: 50) and age gender matched healthy controls were enrolled. All subjects underwent anthropometric measurements (standing height and weight). Mean height (HAZ), weight (WAZ) and body mass index (BAZ) for age Z scores were calculated. Diabetes control was evaluated by measuring glycosylated hemoglobin (HbA1C). Statistical analysis was done by SPSS version 12. Results: Mean age of diabetic children and age gender matched controls was 9.7 ± 4.4 years. Diabetic children were shorter (128.3 ± 24.3 cm vs. 133.6 ± 24.7 cm) and lighter (29.2 kg ± 15.3 vs. 31.3 ± 15.4 kg). HAZ (−1.1 ± 1.2 vs. −0.2 ± 0.8) and WAZ (−1.2 ± 1.3 vs. −0.7 ± 1.3) were significantly lower in diabetic children (P 14 years) were comparable to healthy controls. Conclusions: Growth was compromised in diabetic children in comparison to controls. Children diagnosed at younger age need more attention to optimize growth