Synchronization Strings: Codes for Insertions and Deletions Approaching the Singleton Bound

We introduce synchronization strings as a novel way of efficiently dealing with synchronization errors, i.e., insertions and deletions. Synchronization errors are strictly more general and much harder to deal with than commonly considered half-errors, i.e., symbol corruptions and erasures. For every $\epsilon >0$, synchronization strings allow to index a sequence with an $\epsilon^{-O(1)}$ size alphabet such that one can efficiently transform $k$ synchronization errors into $(1+\epsilon)k$ half-errors. This powerful new technique has many applications. In this paper, we focus on designing insdel codes, i.e., error correcting block codes (ECCs) for insertion deletion channels. While ECCs for both half-errors and synchronization errors have been intensely studied, the later has largely resisted progress. Indeed, it took until 1999 for the first insdel codes with constant rate, constant distance, and constant alphabet size to be constructed by Schulman and Zuckerman. Insdel codes for asymptotically large or small noise rates were given in 2016 by Guruswami et al. but these codes are still polynomially far from the optimal rate-distance tradeoff. This makes the understanding of insdel codes up to this work equivalent to what was known for regular ECCs after Forney introduced concatenated codes in his doctoral thesis 50 years ago. A direct application of our synchronization strings based indexing method gives a simple black-box construction which transforms any ECC into an equally efficient insdel code with a slightly larger alphabet size. This instantly transfers much of the highly developed understanding for regular ECCs over large constant alphabets into the realm of insdel codes. Most notably, we obtain efficient insdel codes which get arbitrarily close to the optimal rate-distance tradeoff given by the Singleton bound for the complete noise spectrum

The SPIRE Photometer Interactive Analysis Package SPIA

The Herschel Common Science System (HCSS) (Ott et al. 2006) (Ott & Science Ground Segment Consortium 2010) is a substantial Java software package, accompanying the development of the Herschel Mission (Pilbratt et al. 2010), supporting all of its phases. In particular the reduction of data from the scientific instruments for instrument checkout, calibration, and astronomical analysis is one of its major applications. The data reduction software is split up in modules, called "tasks". Agreed-upon sequences of tasks form pipelines that deliver well defined standard products for storage in a web-accessible Herschel Science Archive (HSA) (Leon et al. 2009). However, as astronomers and instrument scientists continue to characterize instrumental effects, astronomers already need to publish scientific results and may not have the time to acquire a sufficiently deep understanding of the system to apply necessary fixes. There is a need for intermediate level analysis tools that offer more flexibility than rigid pipelines. The task framework within the HCSS and the highly versatile Herschel Interactive Processing Environment (HIPE), together with the rich set of libraries provide the necessary tools to develop GUI-based interactive analysis packages for the Herschel instruments. The SPIRE Photometer Interactive Analysis (SPIA) package, that was demonstrated in this session, proves the validity of the concept for the SPIRE instrument (Griffin et al. 2010), breaking up the pipeline reduction into logical components, making all relevant processing parameters available in GUIs, and providing a more controlled and user-friendly access to the complexities of the system.Comment: Proceedings accompanying a focus demo given at the ADASS 2010 in Bosto