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Error correction coding schemes with local-global decoding are motivated by practical data storage applications where a balance must be achieved between low latency read access and high data reliability. As an example, consider a 4KB codeword, consisting of four 1KB subblocks, that supports a local-global decoding architecture. Local decoding can provide reliable, low-latency access to individual 1KB subblocks under good channel conditions, while global decoding can provide a “safety-net” for recovery of the entire 4KB block when local decoding fails under bad channel conditions. Recently, Ram and Cassuto have proposed such local-global decoding architectures for LDPC codes and spatially coupled LDPC codes. In this paper, we investigate a coupled polar code architecture that supports both local and global decoding. The coupling scheme incorporates a systematic outer polar code and a partitioned mapping of the outer codeword to semipolarized bit-channels of the inner polar codes. Error rate simulation results are presented for 2 and 4 subblocks. 

Summary In this paper, we develop a systematic theory for high-dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new U-type statistic to test linear hypotheses and establish a high-dimensional Gaussian approximation result under fairly mild moment assumptions. Our general framework and theory can be used to deal with the classical one-way multivariate analysis of variance, and the nonparametric one-way multivariate analysis of variance in high dimensions. To implement the test procedure, we introduce a sample-splitting-based estimator of the second moment of the error covariance and discuss its properties. A simulation study shows that our proposed test outperforms some existing tests in various settings. 

ABSTRACT The scale of post-transcriptional regulation and the implications of its interplay with other forms of regulation in environmental acclimation are underexplored for organisms of the domain Archaea . Here, we have investigated the scale of post-transcriptional regulation in the extremely halophilic archaeon Halobacterium salinarum NRC-1 by integrating the transcriptome-wide locations of transcript processing sites (TPSs) and SmAP1 binding, the genome-wide locations of antisense RNAs (asRNAs), and the consequences of RNase_2099C knockout on the differential expression of all genes. This integrated analysis has discovered that 54% of all protein-coding genes in the genome of this haloarchaeon are likely targeted by multiple mechanisms for putative post-transcriptional processing and regulation, with about 20% of genes likely being regulated by combinatorial schemes involving SmAP1, asRNAs, and RNase_2099C. Comparative analysis of mRNA levels (transcriptome sequencing [RNA-Seq]) and protein levels (sequential window acquisition of all theoretical fragment ion spectra mass spectrometry [SWATH-MS]) for 2,579 genes over four phases of batch culture growth in complex medium generated additional evidence for the conditional post-transcriptional regulation of 7% of all protein-coding genes. We demonstrate that post-transcriptional regulation may act to fine-tune specialized and rapid acclimation to stressful environments, e.g., as a switch to turn on gas vesicle biogenesis to promote vertical relocation under anoxic conditions and modulate the frequency of transposition by insertion sequence (IS) elements of the IS 200 /IS 605 , IS 4 , and IS H3 families. Findings from this study are provided as an atlas in a public Web resource ( https://halodata.systemsbiology.net ). IMPORTANCE While the transcriptional regulation landscape of archaea has been extensively investigated, we currently have limited knowledge about post-transcriptional regulation and its driving mechanisms in this domain of life. In this study, we collected and integrated omics data from multiple sources and technologies to infer post-transcriptionally regulated genes and the putative mechanisms modulating their expression at the protein level in Halobacterium salinarum NRC-1. The results suggest that post-transcriptional regulation may drive environmental acclimation by regulating hallmark biological processes. To foster discoveries by other research groups interested in the topic, we extended our integrated data to the public in the form of an interactive atlas ( https://halodata.systemsbiology.net ).