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We generalize staircase codes and tiled diagonal zipper codes, preserving their key properties while allowing each coded symbol to be protected by arbitrarily many component codewords rather than only two. This generalization which we term "higher-order staircase codes" arises from the marriage of two distinct combinatorial objects: difference triangle sets and finite-geometric nets, which have typically been applied separately to code design. We demonstrate one possible realization of these codes, obtaining powerful, high-rate, low-error-floor, and low-complexity coding schemes based on simple iterative syndrome-domain decoding of coupled Hamming component codes. We anticipate that the proposed codes could improve performance--complexity--latency tradeoffs in high-throughput communications applications, most notably fiber-optic, in which classical staircase codes and zipper codes have been applied. We consider the construction of difference triangle sets having minimum scope and sum-of-lengths, which lead to memory-optimal realizations of higher-order staircase codes. These results also enable memory reductions for early families of convolutional codes constructed from difference triangle sets., Comment: Submitted to IEEE Transactions on Information Theory

We introduce a natural generalization of staircase codes in which each bit is protected by arbitrarily many component codewords rather than two. This enables powerful energy-efficient FEC based on iterative decoding of Hamming components., Comment: Submitted to 2024 Optical Fiber Communication Conference (OFC 2024)

Zipper codes with irregular variable degree are studied. Two new interleaver maps -- chevron and half-chevron -- are described. Simulation results with shortened double-error-correcting Bose--Chaudhuri--Hocquenghem constituent codes show that zipper codes with chevron and half-chevron interleaver maps outperform staircase codes when the rate is below 0.86 and 0.91, respectively, at $10^{-8}$ output bit error rate operating point. In the miscorrection-free decoding scheme, both zipper codes with chevron and half-chevron interleaver maps outperform staircase codes. However, constituent decoder miscorrections induce additional performance gaps., Comment: 6 pages, 11 figures, paper accepted for the GLOBECOM 2023 Workshop on Channel Coding Beyond 5G

We demonstrate, for a widely used model of channels with polarization dependent loss (PDL), that channel capacity is achieved by a simple interference cancellation scheme in conjunction with a universal precoder. Crucially, the proposed scheme is not only information-theoretically optimal, but it is also exceptionally simple and concrete. It transforms the PDL channel into separate scalar additive white Gaussian noise channels, allowing off-the-shelf coding and modulation schemes designed for such channels to approach capacity. The signal-to-noise ratio (SNR) penalty incurred under 6 dB of PDL is reduced to the information-theoretic minimum of a mere 1 dB as opposed to the 4 dB SNR penalty incurred under naive over-provisioning., Comment: Submitted to Journal of Lightwave Technology

Just as rank-metric or Gabidulin codes may be used to construct rate-diversity tradeoff optimal space-time codes, a recently introduced generalization for the sum-rank metric -- linearized Reed-Solomon codes -- accomplishes the same in the case of multiple fading blocks. In this paper, we provide the first explicit construction of minimal delay rate-diversity optimal multiblock space-time codes as an application of linearized Reed-Solomon codes. We also provide sequential decoders for these codes and, more generally, space-time codes constructed from finite field codes. Simulation results show that the proposed codes can outperform full diversity codes based on cyclic division algebras at low SNRs as well as utilize significantly smaller constellations., Comment: Submitted to IEEE Transactions on Information Theory