{'fraction_non_alphanumeric': 0.025559105431309903, 'fraction_numerical': 0.006389776357827476, 'mean_word_length': 5.233830845771144, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Network information flow-multiple sources

We consider the scenario of multicasting a set of information sources in communication networks with multiple senders, multiple encoders and multiple decoders (multi-source multi-sink networks). The information sources are allowed to be encoded within the network, and they are reconstructed by the decoders, where each decoder reconstructs a certain subset of the information sources almost perfectly. We first investigate network coding on acyclic networks in which the reconstruction requirements are arbitrary but the information sources are independent. Inner and outer bounds on the admissible coding rate region are obtained in terms of /spl Gamma/*/sub n/, which is a fundamental region in the entropy space defined by Yeung (1997). Our work extends the work by Yeung and Zhang (1999) on distributed source coding. In addition, we prove that the outer bound for the acyclic single-source single-sink network is tight. We also investigate the multi-source multi-sink network with independent discrete memoryless channels. The admissibility of such a network is characterized under the multicasting requirements that each sink is required to recover all the information sources, which may be correlated.