Real photons produced from photoproduction in pppp collisions

We calculate the production of real photons originating from the photoproduction in relativistic $pp$ collisions. The Weizs$\ddot{\mathrm{a}}$cker-Williams approximation in the photoproduction is considered. Numerical results agree with the experimental data from Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC). We find that the modification of the photoproduction is more prominent in large transverse momentum region.Comment: 2 figure

Photon production in Pb+Pb collisions at sNN\sqrt{s_{NN}}=2.76 TeV

We calculate the high energy photon production from the Pb+Pb collisions for different centrality classes at $\sqrt{s_{NN}}$=2.76 TeV Large Hadron Collider (LHC) energy. The jet energy loss in the jet fragmentation, jet-photon conversion and jet bremsstrahlung is considered by using the Wang-Huang-Sarcevic (WHS) and Baier-Dokshitzer-Mueller-Peigne-Schiff (BDMPS) models. We use the (1+1)-dimensional ideal relativistic hydrodynamics to study the collective transverse flow and space-time evolution of the quark gluon plasma (QGP). The numerical results agree well with the ALICE data of the direct photons from the Pb+Pb collisions ($\sqrt{s_{NN}}$=2.76 TeV) for 0-20\%, 20-40\% and 40-80\% centrality classes.Comment: 4 figure

Stopping Set Distributions of Some Linear Codes

Stopping sets and stopping set distribution of an low-density parity-check code are used to determine the performance of this code under iterative decoding over a binary erasure channel (BEC). Let $C$ be a binary $[n,k]$ linear code with parity-check matrix $H$, where the rows of $H$ may be dependent. A stopping set $S$ of $C$ with parity-check matrix $H$ is a subset of column indices of $H$ such that the restriction of $H$ to $S$ does not contain a row of weight one. The stopping set distribution $\{T_i(H)\}_{i=0}^n$ enumerates the number of stopping sets with size $i$ of $C$ with parity-check matrix $H$. Note that stopping sets and stopping set distribution are related to the parity-check matrix $H$ of $C$. Let $H^{*}$ be the parity-check matrix of $C$ which is formed by all the non-zero codewords of its dual code $C^{\perp}$. A parity-check matrix $H$ is called BEC-optimal if $T_i(H)=T_i(H^*), i=0,1,..., n$ and $H$ has the smallest number of rows. On the BEC, iterative decoder of $C$ with BEC-optimal parity-check matrix is an optimal decoder with much lower decoding complexity than the exhaustive decoder. In this paper, we study stopping sets, stopping set distributions and BEC-optimal parity-check matrices of binary linear codes. Using finite geometry in combinatorics, we obtain BEC-optimal parity-check matrices and then determine the stopping set distributions for the Simplex codes, the Hamming codes, the first order Reed-Muller codes and the extended Hamming codes.Comment: 33 pages, submitted to IEEE Trans. Inform. Theory, Feb. 201