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In this paper, we consider the use of lattice codes over Eisenstein integers for implementing a computeand-forward protocol in wireless networks when channel state information is not available at the transmitter. We extend the compute-and-forward paradigm of Nazer and Gastpar to decoding Eisenstein integer combinations of transmitted messages at relays by proving the existence of a sequence of pairs of nested lattices over Eisenstein integers in which the coarse lattice is good for covering and the fine lattice can achieve the Poltyrev limit. Using this result, we show that both the outage performance and error-correcting performance of nested lattice codebooks over Eisenstein integers surpasses lattice codebooks over integers considered by Nazer and Gastpar with no additional computational complexity. Index TermsCompute-and-Forward, Lattice codes, Eisenstein integers I. INTRODUCTION Compute-and-forward is a novel relaying paradigm in wireless communications in which relays in a network directly compute or decode functions of signals transmitted from multiple transmitters and forward them to a central destination. One of the most effective ways to implement a compute-and-forward scheme is to employ lattice codes at each transmitter. Since a lattice is closed under integer addition, lattice codes are naturally suited to decoding integer linear combinations of transmitted signals.Lattice codes have been shown to be optimal for several problems in communications including coding for the point-to-point additive white Gaussian noise (AWGN) channel [1] and coding with side information problems such as the dirty paper coding problem and Wyner-Ziv problem [2]. The construction of optimal lattice codes for these problems requires a lattice that is good for channel coding. Since a lattice has unconstrained power, goodness for channel coding is measured using Poltyrev's idea of the unconstrained AWGN channel. In [3], Poltyrev derives the maximum noise variance that a lattice can tolerate while maintaining reliable communication over the unconstrained point-to-point AWGN channel, which is referred to as the Poltyrev limit in literature. Loeliger showed the existence of lattices that achieve the Poltyrev limit by means of Construction A in [4]. Then, Erez et al., showed that there exists lattices which are simultaneously good for quantization and can achieve the Poltyrev limit in [5] which made it possible to construct nested lattice codes that were able to achieve a rate of

We evaluated the outcome and optimal management of corrosive esophagitis in 24 children (male:female=8:16, mean age 5.0+/-5.4 years old, ranged from 15 months to 18 years of age) from January 1984 to July 2001. In 20 patients this was the result of accidental ingestion, 4 were suicide attempts and 15 patients (63%) were below 3 years of age. The ingested substances included alkali (n=17, 71%), acid (n=6, 25%), and neutral detergent (n=1, 4%). The "dumpling alkaline oil", a traditional food additive used in Taiwan, was the most common culprit in this study. A total of 9 patients ingested the dumpling alkaline oils, which comprised 38% of the total 24 patients and 53% of the 17 alkaline ingestion accidents. Of the patients 21 (88%) suffered from esophageal injury, and 15 among these 21 patients developed esophageal strictures. Esophageal strictures occurred in all patients with second or third-degree burns. Of these 15 patients with esophageal strictures, 9 (60%) received endoscope-associated dilatation and 6 (40%) underwent an operation (esophagectomy and intestinal interposition). The 9 patients who did not develop esophageal strictures had good body weight gain without feeding difficulty (functionally normal recovery). On the other hand, among the 15 patients with esophageal strictures, 9 patients had functionally subnormal recovery and 6 patients had poor recovery with either frequent feeding difficulty or growth retardation. In conclusion, accidental ingestion of alkaline oil is the most common cause of corrosive esophagitis in Taiwan. The degree of burns correlated with stricture formation.

Background and Objectives-During laser therapy of port wine stain (PWS) birthmarks, regions of persistent perfusion may exist. Immediate retreatment of such regions may improve PWS laser therapeutic outcome. To address this need, we propose use of laser speckle imaging (LSI) to provide real-time, quantitative feedback during laser surgery. Herein, we present in vitro and in vivo data collected with a clinic-based LSI instrument.

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Background Pulsed dye laser is the gold standard for treatment of port wine stain birthmarks but multiple treatments are required and complete resolution is often not achieved. Post-treatment vessel recurrence is thought to be a factor that limits efficacy of pulsed dye laser treatment of port wine stains. Imiquimod 5% cream is an immunomodulator with anti-angiogenic effects. Objective To determine if application of imiquimod 5% cream after pulsed dye laser improves treatment outcome. Methods Healthy patients with port wine stains (n = 24) were treated with pulsed dye laser and then randomized to apply post-treatment placebo or imiquimod 5% cream for 8 weeks. Chromameter measurements (CIE L*a*b* colorspace) for 57 port wine stain sites (multiple sites per subject) were taken at baseline and compared with measurements taken 8 weeks post-treatment. The change in a* and ΔE were measured to quantify treatment outcome. Results Two subjects developed minor skin irritation. Other adverse effects weren't noted. Average Δa* was 0.43 for pulsed dye laser + placebo sites (n = 25) and 1.27 for pulsed dye laser + imiquimod sites (n = 32) (p value = 0.0294) indicating a greater reduction in erythema with imiquimod. Average ΔE was 2.59 for pulsed dye laser + placebo and 4.08 for pulsed dye laser + imiquimod (p value = 0.0363), again indicating a greater color improvement with imiquimod. Limitations Effects were evaluated after a single treatment and duration of effect is unknown. Conclusion Combined selective photothermolysis and anti-angiogenic therapy may enhance port wine stain treatment efficacy.

Abstract-In this paper, we propose a new downlink nonorthogonal multiuser superposition transmission scheme for future 5G cellular networks, which we refer to as the lattice partition multiple access (LPMA). In this proposed design, the base station transmits multilevel lattice codes for multiple users. Each user's code level corresponds to a distinct prime and is weighted by a product of all distinct primes of the other users excluding its own. Due to the structural property of lattice codes, each user can cancel out the interference from the other code levels by using the modulo lattice operation in a successive/parrallel manner. LPMA can overcome the drawback of non-orthogonal multiple access (NOMA), which arises when users have similar channel conditions. We demonstrate that the proposed LPMA shows a clear throughput enhancement over the current NOMA scheme.

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