Probabilistic Shaping for Trellis-Coded Modulation With CRC-Aided List Decoding

Linfang Wang

doi:10.1109/TCOMM.2023.3237263

Probabilistic Shaping for Trellis-Coded Modulation With CRC-Aided List Decoding

2023-03-01

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DOI：10.1109/TCOMM.2023.3237263

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This paper applies probabilistic amplitude shaping (PAS) to cyclic redundancy check (CRC)-aided tail-biting trellis-coded modulation (TCM). CRC-TCM-PAS produces practical codes for short block lengths on the additive white Gaussian noise (AWGN) channel. In the transmitter, equally likely message bits are encoded by a distribution matcher (DM) generating amplitude symbols with a desired distribution. A CRC is appended to the sequence of amplitude symbols, and this sequence is then encoded and modulated by TCM to produce real-valued channel input signals. This paper proves that the sign values produced by the TCM are asymptotically equally likely to be positive or negative. The CRC-TCM-PAS scheme can thus generate channel input symbols with a symmetric capacity-approaching probability mass function. The paper provides an analytical upper bound on the frame error rate of the CRC-TCM-PAS system over the AWGN channel. This FER upper bound is the objective function used for jointly optimizing the CRC and convolutional code. Additionally, this paper proposes a multi-composition DM, which is a collection of multiple constant-composition DMs. The optimized CRC-TCM-PAS systems achieve frame error rates below the random coding union (RCU) bound in AWGN and outperform the short-blocklength PAS systems with various other forward error correction codes studied in Coskun et al. (2019).

Keywords:

Reliable communication

short blocklength

probabilistic shaping

trellis-coded modulation

tail-biting convolutional code

CRC

list decoding

distribution matcher

Probabilistic Shaping for Trellis-Coded Modulation With CRC-Aided List Decoding

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