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			<titleStmt><title level='a'>Shaped TCM with List Decoding that Exceeds the RCU Bound by Optimizing a Union Bound on FER</title></titleStmt>
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				<publisher>IEEE</publisher>
				<date>12/04/2022</date>
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				<bibl> 
					<idno type="par_id">10398495</idno>
					<idno type="doi">10.1109/GLOBECOM48099.2022.10000695</idno>
					<title level='j'>GLOBECOM 2022 - 2022 IEEE Global Communications Conference</title>
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					<author>Dan Song</author><author>Felipe Areces</author><author>Linfang Wang</author><author>Richard Wesel</author>
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			<abstract><ab><![CDATA[This paper derives a union bound on the frame error rate (FER) of a probabilistic amplitude shaping (PAS) system which uses a CRC-aided,  rate −k/k+1 , systematic, recursive trellis-coded modulation (TCM). A tail-biting convolutional code (TBCC) provides the feed-forward error correction (FEC) code for the TCM. The system is referred as CRC-TCM-PAS [1]. In order to derive the union bound, we first prove that the concatenation of a CRC and a  rate −k/k+1 convolutional code is equivalent to a new convolutional code. Then, we give the generating function of the new convolutional code using Biglieri's product-state-diagram approach. A union bound can be calculated using the generating function. Simulation results show that the derived union bound is tight in the high signal-to-noise ratio (SNR) regime and can be used to design the convolutional and CRC codes. Simulation results also show that the optimized CRC-TCM-PAS system exceeds the random coding union (RCU) bound and outperforms the PAS systems with various FEC codes studied in [2] for the same number of input bits and the same transmission rate.]]></ab></abstract>
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