This paper proposes a novel representation, known as Lv's distribution (LVD), of linear frequency modulated (LFM) signals. It has been well known that a monocomponent LFM signal can be uniquely determined by two important physical quantities, centroid frequency and chirp rate (CFCR). The basic reason for expressing a LFM signal in the CFCR domain is that these two quantities may not be apparent in the time or time-frequency (TF) domain. The goal of the LVD is to naturally and accurately represent a mono-or multicomponent LFM in the CFCR domain. The proposed LVD is simple and only requires a two-dimensional (2-D) Fourier transform of a parametric scaled symmetric instantaneous autocorrelation function. It can be easily implemented by using the complex multiplications and fast Fourier transforms (FFT) based on the scaling principle. The computational complexity, properties, detection performance and representation errors are analyzed for this new distribution. Comparisons with three other popular methods, Radon-Wigner transform (RWT), Radon-Ambiguity transform (RAT), and fractional Fourier transform (FRFT) are performed. With several numerical examples, our distribution is demonstrated to be a CFCR representationthat is computed without using any searching operation. The main significance of the LVD is to convert a 1-D LFM into a 2-D single-frequency signal. One of the most important applications of the LVD is to generate a new TF representation, called inverse LVD (ILVD), and a new ambiguity function, called Lv's ambiguity function (LVAF), both of which may break through the tradeoff between resolution and cross terms.

yxmao@ouc.edu.cn or fenghen360@126.com.

Low-density parity-check (LDPC) codes have attracted much attention in the past two decades since they can asymptotically approach the Shannon capacity in a variety of data transmission and storage scenarios. As a type of promising structured LDPC codes, the protograph LDPC codes not only inherit the advantage of conventional LDPC codes, i.e., excellent error performance, but also possess simple representations to realize fast encoding and efficient decoding. This paper provides a comprehensive survey on the state-of-the-art in protograph LDPC code design and analysis for different channel conditions, including the additive white Gaussian noise (AWGN) channels, fading channels, partial response (PR) channels, and Poisson pulse-position modulation (PPM) channels. Moreover, the applications of protograph LDPC codes to joint sourceand-channel coding (JSCC) and joint channel-and-physical-layernetwork coding (JCPNC) are reviewed and studied. In particular, we focus our attention on the encoding design and assume the decoder is implemented by the belief propagation (BP) algorithm. Hopefully, this survey may facilitate the research in this area.

The ancient gymnosperm genus Taxus is the exclusive source of the anticancer drug paclitaxel, yet no reference genome sequences are available for comprehensively elucidating the paclitaxel biosynthesis pathway. We have completed a chromosome-level genome of Taxus chinensis var. mairei with a total length of 10.23 gigabases. Taxus shared an ancestral whole-genome duplication with the coniferophyte lineage and underwent distinct transposon evolution. We discovered a unique physical and functional grouping of CYP725As (cytochrome P450) in the Taxus genome for paclitaxel biosynthesis. We also identified a gene cluster for taxadiene biosynthesis, which was formed mainly by gene duplications. This study will facilitate the elucidation of paclitaxel biosynthesis and unleash the biotechnological potential of Taxus.