{'fraction_non_alphanumeric': 0.022017045454545456, 'fraction_numerical': 0.0, 'mean_word_length': 5.234513274336283, '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}}
Shannon capacity of frequency-overlapped digital subscriber loop channels

The Shannon capacity equation defines the total data transmission capacity of a transmission channel as a function of receiver SNR and bandwidth. When the frequency-overlapped (FO) duplex mode of operation with an echo canceller is implemented on a digital subscriber loop (DSL) channel, then the near-end receiver SNR that determines the inbound capacity is not only a function of the far-end transmitted signal power, but also of the residual near-end transmit signal power that leaks through the echo canceller. This 'coupling' occurs on both ends of the copper loop for upstream and downstream reception. Consequently, maximization of the data transmission capacity is a "bidirectional" problem. This problem has not been analyzed in the literature. We define the notion of the total bidirectional data capacity of a copper loop and formulate the maximum bidirectional capacity that can be achieved when a power budget is allocated to each of the two transmitters. We then compute the channel capacity by an integer linear programming (ILP) technique for various channel and noise conditions and also compare the results with the data rates that are obtained by a modified "water-filling" algorithm designed for FO duplex operation and with the channel capacities of the conventional frequency-division (FD) simplex transmission.