arXiv subjects
Publications and source records attributed to William Kingsford.
We provide some difference triangle sets with scopes that improve upon the best known values. These are found with purpose-built digital circuits realized with field-programmable gate arrays (FPGAs) rather than software algorithms running on general-purpose processors.
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.