Twitter is a widely used online social media. One important characteristic of Twitter is its real-time nature. In this paper, we investigate whether the daily number of tweets that mention Standard & Poor 500 (S&P 500) stocks is correlated with S&P 500 stock indicators (stock price and traded volume) at three different levels, from the stock market to industry sector and individual company stocks. We further apply a linear regression with exogenous input model to predict stock market indicators, using Twitter data as exogenous input. Our preliminary results demonstrate that daily number of tweets is correlated with certain stock market indicators at each level. Furthermore, it appears that Twitter is helpful to predict stock market. Specifically, at the stock market level, we find that whether S&P 500 closing price will go up or down can be predicted more accurately when including Twitter data in the model.

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Digital fountain codes are record-breaking codes for erasure channels. They have many potential applications in both wired and wireless communications. Most existing digital fountain codes operate over binary fields using an iterative belief-propagation (BP) decoding algorithm. In this paper, we propose a new iterative decoding algorithm for both binary and nonbinary fields. The basic form of our proposed algorithm considers both degree-1 and degree-2 check nodes (instead of only degree-1 check nodes as in the original BP decoding scheme), and has linear complexity. Extensive simulation demonstrates that it outperforms the original BP decoding scheme, especially for a small number of source packets. The enhanced form of the proposed algorithm combines the basic form of the algorithm and a guess-based algorithm to further improve the decoding performance. Simulation results demonstrate that it can provide better decoding performance than the guess-based algorithm with fewer guesses, and can achieve decoding performance close to that of the maximum likelihood decoder at a much lower decoding complexity. Last, we show that our nonbinary scheme has the potential to outperform the binary scheme when choosing suitable degree distributions, and furthermore it is insensitive to the size of the Galois field.

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