{'fraction_non_alphanumeric': 0.018867924528301886, 'fraction_numerical': 0.0, 'mean_word_length': 5.044303797468355, '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}}
Relaying simultaneous multicasts via structured codes

Simultaneous multicasting of messages with the help of a relay is studied. A two-source two-destination network is considered, in which each destination can receive directly only the signal from one of the sources, so that the reception of the message from the other source (and multicasting) is enabled by the presence of the relay. An outer bound is derived, which is shown to be achievable in the case of finite-field modulo-additive channels by using linear codes, highlighting the benefits of structured codes in exploiting the underlying physical-layer structure of the network. Results are extended to the Gaussian channel model as well, providing achievable rate regions based on nested lattice codes. It is shown that for a wide range of power constraints, the performance with lattice codes approaches the upper bound and surpasses the rates achieved by the standard random coding schemes.