{'fraction_non_alphanumeric': 0.022094140249759846, 'fraction_numerical': 0.004803073967339097, 'mean_word_length': 5.553459119496855, '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}}
Serial concatenation of Hermitian codes with ring‐TCM codes

Hermitian codes are a class of very long algebraic‐geometric (AG) codes constructed from Hermitian curves, which outperform Reed–Solomon codes defined over the same finite fields and with the same code rates, as recently demonstrated by the authors. However, since there are no soft‐decision decoding algorithms for AG codes in the literature, the performance of Hermitian codes is limited and their potential is yet to be realized. An alternative method for achieving more significant coding gains is presented in this paper by serially concatenating long Hermitian codes with ring‐trellis‐coded modulation codes over the ring of integers ℤ4 and evaluating their performance through simulation results on the AWGN and Rayleigh fading channels. The scheme achieves large coding gains over single Hermitian and Reed–Solomon codes with no increase in bandwidth use and a performance comparable with the well‐known capacity‐approaching codes. Copyright © 2007 John Wiley & Sons, Ltd.