Synchrotron spectrum of fast cooling electrons in GRBs

We discuss the synchrotron emission of fast cooling electrons in shocks. The fast cooling electrons behind the shocks can generate a position-dependent inhomogeneous electron distribution if they do not have enough time to mix homogeneously. This would lead to a very different synchrotron spectrum in low-frequency bands to that in the homogeneous case due to the synchrotron absorption. In this paper, we calculate the synchrotron spectrum in the inhomogeneous case in a gamma-ray burst (GRB). Both the forward shock and the reverse shock are considered. We find for the reverse shock dominated case, we would expect a "reverse shock bump" in the low-frequency spectrum. The spectral bump is due to the combination synchrotron absorption in both the forward and reverse shock regions. In the forward shock spectrum in the low frequencies has two unconventional segments with spectral slopes of $\lesssim1$ and $11/8$. The slope of $11/8$ has been found by some authors, while the slope of $\lesssim1$ is new, which is due to the approximately constant electron temperature in the optically thick region. In the future, simultaneous observations in multiple bands (especially in the low frequency bands) in the GRB early afterglow or prompt emission phases will possibly reveal these spectral characteristics and enable us to identify the reverse shock component and distinguish between the forward and reverse shock emissions. This also may be a method with which to diagnose the electron distribution status (homogeneous or inhomogeneous) after fast cooling in the relativistic shock region.Comment: Published in ApJ, 839, 74 (7pp), 2017, Apri

Block Markov Superposition Transmission of RUN Codes

In this paper, we propose a simple procedure to construct (decodable) good codes with any given alphabet (of moderate size) for any given (rational) code rate to achieve any given target error performance (of interest) over additive white Gaussian noise (AWGN) channels. We start with constructing codes over groups for any given code rates. This can be done in an extremely simple way if we ignore the error performance requirement for the time being. Actually, this can be satisfied by repetition (R) codes and uncoded (UN) transmission along with time-sharing technique. The resulting codes are simply referred to as RUN codes for convenience. The encoding/decoding algorithms for RUN codes are almost trivial. In addition, the performance can be easily analyzed. It is not difficult to imagine that a RUN code usually performs far away from the corresponding Shannon limit. Fortunately, the performance can be improved as required by spatially coupling the RUN codes via block Markov superposition transmission (BMST), resulting in the BMST-RUN codes. Simulation results show that the BMST-RUN codes perform well (within one dB away from Shannon limits) for a wide range of code rates and outperform the BMST with bit-interleaved coded modulation (BMST-BICM) scheme.Comment: submitted to IEEE Transactions on Communication

Decoding and Computing Algorithms for Linear Superposition LDPC Coded Systems

This paper is concerned with linear superposition systems in which all components of the superimposed signal are coded with an identical binary low-density parity-check (LDPC) code.Comment: The simulation in Fig.5 is not correc

Systematic Block Markov Superposition Transmission of Repetition Codes

In this paper, we propose systematic block Markov superposition transmission of repetition~(BMST-R) codes, which can support a wide range of code rates but maintain essentially the same encoding/decoding hardware structure. The systematic BMST-R codes resemble the classical rate-compatible punctured convolutional~(RCPC) codes, except that they are typically non-decodable by the Viterbi algorithm due to the huge constraint length induced by the block-oriented encoding process. The information sequence is partitioned equally into blocks and transmitted directly, while their replicas are interleaved and transmitted in a block Markov superposition manner. By taking into account that the codes are systematic, we derive both upper and lower bounds on the bit-error-rate~(BER) under maximum {\em a posteriori}~(MAP) decoding. The derived lower bound reveals connections among BER, encoding memory and code rate, which provides a way to design good systematic BMST-R codes and also allows us to make trade-offs among efficiency, performance and complexity. Numerical results show that:~1)~the proposed bounds are tight in the high signal-to-noise ratio~(SNR) region;~2)~systematic BMST-R codes perform well in a wide range of code rates, and~3)~systematic BMST-R codes outperform spatially coupled low-density parity-check~(SC-LDPC) codes under an equal decoding latency constraint.Comment: Submitted to IEEE Trans. Inf. Theor

Speaker Verification By Partial AUC Optimization With Mahalanobis Distance Metric Learning

Receiver operating characteristic (ROC) and detection error tradeoff (DET) curves are two widely used evaluation metrics for speaker verification. They are equivalent since the latter can be obtained by transforming the former's true positive y-axis to false negative y-axis and then re-scaling both axes by a probit operator. Real-world speaker verification systems, however, usually work on part of the ROC curve instead of the entire ROC curve given an application. Therefore, we propose in this paper to use the area under part of the ROC curve (pAUC) as a more efficient evaluation metric for speaker verification. A Mahalanobis distance metric learning based back-end is applied to optimize pAUC, where the Mahalanobis distance metric learning guarantees that the optimization objective of the back-end is a convex one so that the global optimum solution is achievable. To improve the performance of the state-of-the-art speaker verification systems by the proposed back-end, we further propose two feature preprocessing techniques based on length-normalization and probabilistic linear discriminant analysis respectively. We evaluate the proposed systems on the major languages of NIST SRE16 and the core tasks of SITW. Experimental results show that the proposed back-end outperforms the state-of-the-art speaker verification back-ends in terms of seven evaluation metrics

Spatial Coupling of Generator Matrix: A General Approach to Design of Good Codes at a Target BER

For any given short code (referred to as the basic code), block Markov superposition transmission (BMST) provides a simple way to obtain predictable extra coding gain by spatial coupling the generator matrix of the basic code. This paper presents a systematic design methodology for BMST systems to approach the channel capacity at any given target bit-error-rate (BER) of interest. To simplify the design, we choose the basic code as the Cartesian product of a short block code. The encoding memory is then inferred from the genie-aided lower bound according to the performance gap of the short block code to the corresponding Shannon limit at the target BER. In addition to the sliding-window decoding algorithm, we propose to perform one more phase decoding to remove residual (rare) errors. A new technique that assumes a noisy genie is proposed to upper bound the performance. Under some mild assumptions, these genie-aided bounds can be used to predict the performance of the proposed two-phase decoding algorithm in the extremely low BER region. Using the Cartesian product of a repetition code as the basic code, we construct a BMST system with an encoding memory 30 whose performance at the BER of $10^{-15}$ can be predicted within one dB away from the Shannon limit over the binary-input additive white Gaussian noise channel (BI-AWGNC)

A Riemannian Inexact Newton-CG Method for Nonnegative Inverse Eigenvalue Problems: Nonsymmetric Case

This paper is concerned with the nonnegative inverse eigenvalue problem of finding a nonnegative matrix such that its spectrum is the prescribed self-conjugate set of complex numbers. We first reformulate the nonnegative inverse eigenvalue problem as an under-determined constrained nonlinear matrix equation over several matrix manifolds. Then we propose a Riemannian inexact Newton-CG method for solving the nonlinear matrix equation. The global and quadratic convergence of the proposed method is established under some mild conditions. We also extend the proposed method to the case of prescribed entries. Finally, numerical experiments are reported to illustrate the efficiency of the proposed method.Comment: 24 page

On neutral scalar radiation by a massive orbiting star in extremal Kerr-Newman black hole

In this short note we extend the work of 1401.3746 about gravity waves by a massive orbiting star in an extremal Kerr black hole to an extremal Kerr- Newman black hole for scalar radiation, and still find that it has a CFT interpretation from Kerr-Newman/CFT. In addition, we investigate on electromagnetic radiation with Kerr/CFT, which a detailed analysis isn't given by 1401.3746.Comment: 13 pages, no figures. Some typos correcte

A New Class of Multiple-rate Codes Based on Block Markov Superposition Transmission

Hadamard transform~(HT) as over the binary field provides a natural way to implement multiple-rate codes~(referred to as {\em HT-coset codes}), where the code length $N=2^p$ is fixed but the code dimension $K$ can be varied from $1$ to $N-1$ by adjusting the set of frozen bits. The HT-coset codes, including Reed-Muller~(RM) codes and polar codes as typical examples, can share a pair of encoder and decoder with implementation complexity of order $O(N \log N)$. However, to guarantee that all codes with designated rates perform well, HT-coset coding usually requires a sufficiently large code length, which in turn causes difficulties in the determination of which bits are better for being frozen. In this paper, we propose to transmit short HT-coset codes in the so-called block Markov superposition transmission~(BMST) manner. At the transmitter, signals are spatially coupled via superposition, resulting in long codes. At the receiver, these coupled signals are recovered by a sliding-window iterative soft successive cancellation decoding algorithm. Most importantly, the performance around or below the bit-error-rate~(BER) of $10^{-5}$ can be predicted by a simple genie-aided lower bound. Both these bounds and simulation results show that the BMST of short HT-coset codes performs well~(within one dB away from the corresponding Shannon limits) in a wide range of code rates

Serial Concatenation of RS Codes with Kite Codes: Performance Analysis, Iterative Decoding and Design

In this paper, we propose a new ensemble of rateless forward error correction (FEC) codes. The proposed codes are serially concatenated codes with Reed-Solomon (RS) codes as outer codes and Kite codes as inner codes. The inner Kite codes are a special class of prefix rateless low-density parity-check (PRLDPC) codes, which can generate potentially infinite (or as many as required) random-like parity-check bits. The employment of RS codes as outer codes not only lowers down error-floors but also ensures (with high probability) the correctness of successfully decoded codewords. In addition to the conventional two-stage decoding, iterative decoding between the inner code and the outer code are also implemented to improve the performance further. The performance of the Kite codes under maximum likelihood (ML) decoding is analyzed by applying a refined Divsalar bound to the ensemble weight enumerating functions (WEF). We propose a simulation-based optimization method as well as density evolution (DE) using Gaussian approximations (GA) to design the Kite codes. Numerical results along with semi-analytic bounds show that the proposed codes can approach Shannon limits with extremely low error-floors. It is also shown by simulation that the proposed codes performs well within a wide range of signal-to-noise-ratios (SNRs).Comment: 34 pages, 15 figure