Calvin Lab Auditorium
Product codes were introduced by Elias in 1954 and generalized by Tanner in 1981. Recently, a number of generalized product codes have been proposed for forward error-correction in high-speed optical communication. In practice, these codes are decoded by iteratively decoding each of the component codes. Symmetric product codes are a subclass of generalized product codes that use symmetry to reduce the block length to roughly half that of a product code with the same component code. When compared to a product code of similar length and rate, this modification can result in improved performance in both the waterfall region and the error floor. A special case of these codes was introduced by Tanner in 1981 and recently called a half-product code by Justesen in 2011. In this talk, we discuss some initial results on symmetric product codes. Our results show that (i) these codes have a larger normalized minimum distance than the product code from which they are derived, (ii) some small constructions achieve the best parameters possible with a linear code, and (iii) extending the construction to tightly-braided block codes achieves similar gains.