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Sparse code multiple access (SCMA) is one of the competitive non-orthogonal multiple access (NOMA) techniques for the next generation communication systems. In this paper, we put forward a simple and efficient design method named divided extended mother codebook (DEMC) to construct SCMA codebooks based on golden angle modulation (GAM) constellation points. First, we generate a vector defined by the GAM. Second, we design the extended mother codebook ( $\mathbf {EMC}$ ) by introducing the power and phase dependent constraints of symbols in multi-dimension codewords. The power constraints can ensure the power of each codeword is the same which leads to the optimal peak to average power ratio (PAPR) especially for the uplink channel. Third, we divide the $\mathbf {EMC}$ into several mother codebooks ( $\mathbf {MC}\text{s}$ ) to generate the constant bit rate (CBR) or variable bit rate (VBR) SCMA codebooks. The structure of the VBR SCMA codebooks is compatible with that of CBR. The VBR codebooks and CBR codebooks use the same factor graph, therefore, the users employed the VBR codebooks can also utilize the efficient message passing algorithm (MPA) for multi-user detection. Simulations reveal that the bit error rate (BER) performance of the proposed CBR DEMC-SCMA codebooks is outstanding with low complexity. The VBR DEMC-SCMA codebooks can flexibly satisfy the different service requirements, and the BER performance of the VBR DEMC-SCMA codebooks is close to each other though their modulation orders are various. This feature shows that the users can apply for a high order codebook to get a faster information transfer rate without increasing transmission power and bandwidth.

Wallenberg syndrome is the most common stroke of the posterior circulation. Diagnosis of Wallenberg syndrome is often overlooked as initial MRI may show no visible lesion. We present an atypical case of Wallenberg syndrome in which the initial MRI of the brain was normal. Our patient is a 65-year-old male who was brought in by emergency medical services complaining of right-sided facial droop, slurred speech, and left-sided weakness for one day. Physical examination showed decreased left arm and leg strength compared to the right side, decreased left facial temperature sensations, decreased left arm and leg temperature sensations, and difficulty sitting upright with an associated leaning towards the left side. An initial magnetic resonance imaging (MRI) of the brain with and without contrast revealed no abnormality. In light of such a high suspicion for stroke based on the patient’s neurologic deficits, a repeat MRI of the brain was performed three days later and exposed a small focus of bright signal (hyperintensity) on T2-weighted fluid-attenuated inversion recovery and diffusion-weighted imaging (DWI) in the left posterior medulla. Wallenberg syndrome, also known as lateral medullary syndrome or posterior inferior cerebellar artery syndrome, is a constellation of symptoms caused by posterior vascular accidents. The neurological deficits associated with this disease are due to damage of the lateral medulla, inferior cerebellar peduncle, nucleus of trigeminal nerve, nucleus and fibers of vagus and glossopharyngeal nerves, descending sympathetic tract, spinothalamic tract, and/or vestibular nuclei. MRI with DWI is the gold standard to confirm the diagnosis. Wallenberg syndrome has the potential to leave patients extremely debilitated. Early detection, management, and rehabilitation are critical for improving post-stroke recovery.

In this study, we propose a method named decomposition of the superposed constellation (DCSC) to design sparse code multiple access (SCMA) codebooks for the additive white Gaussian noise (AWGN) channel. We prove that the power of the user symbols (USs) is accurately determined by the power of the superposed constellation (SC). Thus, we select quadrature amplitude modulation (QAM) constellations as the SC and decompose the SC into several groups of USs with power diversity. The minimum Euclidean distance (MED) between superposed symbols (SS-MED) in the receiver is determined by the selected QAM and MED between the multi-dimensional codewords (CW-MED) is optimized by matching the symbols on different dimensions. We propose a simplified DCSC (S-DCSC) by modifying the factor graph and avoiding the transmission of USs with low power, which greatly reduces the complexity of the message passing algorithm (MPA). The simulations show that the SS-MEDs of DCSC and S-DCSC are larger than those in previous papers and the BER performance of the proposed codebooks is better than others.