Gou Hosoya

Bit-interleaved coded modulation (BICM) with Gray labeling is widely used, yet its mismatched decoding metric keeps achievable rates below the coded modulation (CM) capacity, which multilevel coding attains only with multiple component codes. Delayed BICM (DBICM) bridges this gap with a single encoder and decoder by delaying coded bit subsequences so that already-decoded bits act as side information; for staircase delay vectors, its middle-region rate provably equals the CM capacity for any labeling. Under continuous transmission, however, initial and final codewords share symbols with pilot bits, and these boundary rates depend strongly on the pilot values. For pulse amplitude modulation, we design delay vectors and boundary pilots that keep every boundary rate at or above the middle-region capacity. For set-partitioning (SP) labeling, a closed-form minimum-shift pilot rule provably guarantees this condition for every staircase vector and SNR, whereas Gray labeling admits capacity-preserving pilots found by numerical search up to 32-PAM. Density evolution predicts gains approaching 1 dB over rate-matched BICM baselines for both labelings. Long continuous simulations, however, reveal severe inter-codeword error propagation under SP labeling, establishing Gray labeling as the practical choice. With per-level irregular LDPC codes, DBICM retains consistent threshold and waterfall gains at identical effective rates.