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Land use and land cover change (LULCC), along with the conversion of natural ecosystem cover into farmland, poses significant ecological challenges for desert riparian ecosystems. The Tarim River Basin (TRB), home to the world's largest and most densely distributed and well-preserved desert riparian ecosystem, remains exceptionally susceptible to climate change. However, our understanding of the role of climatic factors (mean annual temperature (MAT); mean temperature during the warmest month (MWMT); relative humidity in September, October, and November (RH_SON); and the annual heat–moisture index (AHM)) in driving pattern changes in these ecosystems remains limited. To address this gap, we employed a transfer matrix approach coupled with geographically weighted regression models to conduct an extensive analysis of LULCC trends and their driving factors within the TRB from 1990 to 2020. The 30-year dataset on LULCC provided invaluable insights, revealing that the proliferation of farmland and shrubberies has precipitated the decline of arbor forests and grassland expanses. Furthermore, this expansion of farmland and shrubberies has resulted in heightened ecosystem fragmentation, particularly notable between 2005 and 2010. Our assessment indicates that artificial ecosystems are gradually transitioning back into natural states, encompassing 8.24% of the total area, chiefly attributed to the expanding shrubbery regions. Additionally, in-depth scrutiny of the impacts of climatic factors on ecosystem structure unveiled that moisture exerts the most pronounced influence on ecosystem patterns, followed by air moisture content during the growing season, while temperature exerts a relatively lesser impact. Overall, this study contributes to the realization of SDG 13 (Climate Action) and SDG 15 (Life on Land) by informing conservation efforts and sustainable land management practices in dryland desert riparian ecosystems. [ABSTRACT FROM AUTHOR]

For the decoding of a binary linear block code of minimal Hamming distance d over additive white Gaussian noise (AWGN) channels, a soft-decision decoder achieves bounded-distance (BD) decoding if its squared error-correction radius is equal to d. A Chase-like algorithm outputs the best (most likely) codeword in a list of candidates generated by a conventional algebraic binary decoder in a few trials. It is of interest to design Chase-like algorithms that achieve BD decoding with as least trials as possible. In this paper, we show that Chase-like algorithms can achieve BD decoding with only O([d.sup.1/2+[epsilon]]) trials for any given positive number [epsilon]. Index Terms--Algebraic binary decoder, asymptotical optimality, bounded-distance (BD) decoding, Chase-like algorithm, maximum-likelihood (ML) decoding, reliability-order-based decoding algorithm (ROBDA).

In this correspondence, we consider the decoding of binary block codes over the additive white Gaussian noise (AWGN) channel with binary phase-shift keying (BPSK) signaling. By a reliability-order-based decoding algorithm (ROBDA), we mean a soft-decision decoding algorithm which decodes to the best (most likely) codeword of the form that is the sum of the hard-decision tuple and an error pattern in a set determined only by the order of the reliabilities of the hard decisions. Examples of ROBDAs include many well-known decoding algorithms, such as the generalized-minimum-distance (GMD) decoding algorithm, Chase decoding algorithms, and the reliability-based decoding algorithms proposed by Fossorier and Lin. It is known that the squared error-correction-radii of ROBDAs can be computed from the minimal squared Euclidean distances (MSEDs) between the all-one sequence and the polyhedra corresponding to the error patterns. For the computation of such MSEDs, we give a new method which is more compact than the one proposed by Fossorier and Lin. These results are further used to show that any bounded-distance ROBDA is asymptotically optimal: The ratio between the probability of decoding error of a bounded-distance ROBDA and that of the maximum-likelihood (ML) decoding approaches 1 when the signal-to-noise ratio (SNR) approaches infinity, provided that the minimum Hamming distance of the code is greater than 2. Index Terms--Asymptotic optimality, bounded-distance decoding, error performance, linear block codes, maximum-likelihood (ML) decoding, reliability-order-based decoding.

The generalized minimum distance (GMD) and Chase decoding algorithms are some of the most important suboptimum bounded distance decoding algorithms for the binary linear block codes over an additive white Gaussian noise (AWGN) channel. In this correspondence, we compute the limitation of the ratio between the probability of decoding error for the GMD or any one of the Chase decoding algorithms and that of the maximum-likelihood (ML) decoding when the signal-to-noise ratio (SNR) approaches infinity. If the minimum Hamming distance of the code is greater than 2, the limitation is shown to be equal to 1 and thus the GMD and Chase decoding algorithms are asymptotically optimum. Index Terms--Asymptotic optimality, binary linear block code, bounded distance decoding, error performance, maximum-likelihood (ML) decoding.

Let p be an odd prime, m and k be positive integers such that s = m / e is odd and k / e is even, where e = gcd ⁡ ( m , k ) . In this paper, the value distribution of the exponential sum ∑ x ∈ F p m χ ( α x ( p k + 1 ) ( p m + 1 ) / 4 + β x ) is completely determined with p m ≡ 1 ( mod 4 ) . As applications, when p m ≡ 1 ( mod 4 ) , the distribution of the cross correlation between a p -ary m -sequence ( s t ) of period p m − 1 and its decimated sequence ( s d t ) with d = ( p k + 1 ) ( p m + 1 ) / 4 is determined. The sequence family F is constructed and the cross correlation distribution among sequences in the family F is also determined. Our result shows that the maximal magnitude of the correlation value is low when e = 1 . [ABSTRACT FROM AUTHOR]

For integer k ≥ 2 and prime power q , Lazebnik and Ustimenko (1995) proposed an algebraic bipartite graph D ( k , q ) which is q -regular, edge-transitive and of large girth. Füredi et al. (1995) conjectured that D ( k , q ) has girth k + 5 for all odd k and all q ≥ 4 and, shown that this conjecture is true for the case that ( k + 5 ) / 2 divides q − 1 . Cheng et al. (2014) shown that this conjecture is true for the case that ( k + 5 ) / 2 is an arbitrary power of the characteristic of F q . In this paper, we propose a generalization for the binomial coefficients and show that this conjecture is true when ( k + 5 ) / 2 is the product of an arbitrary factor of q − 1 and an arbitrary power of the characteristic of F q . [ABSTRACT FROM AUTHOR]

For integer k ≥ 2 and prime power q , an algebraic bipartite graph D ( k , q ) of girth at least k + 4 was introduced by Lazebnik and Ustimenko (1995). Füredi et al. (1995) shown that the girth of D ( k , q ) is equal to k + 5 if k is odd and q is a prime power of form 1 + n ( k + 5 ) / 2 and, conjectured further that D ( k , q ) has girth k + 5 for all odd k and all q ≥ 4 . In this paper, we show that this conjecture is true when ( k + 5 ) / 2 is a power of the characteristic of F q . [ABSTRACT FROM AUTHOR]