Codes for Correcting Asymmetric Adjacent Transpositions and Deletions

Codes in the Damerau--Levenshtein metric have been extensively studied recently owing to their applications in DNA-based data storage. In particular, Gabrys, Yaakobi, and Milenkovic (2017) designed a length-$n$ code correcting a single deletion and $s$ adjacent transpositions with at most $(1+2s)\log n$ bits of redundancy. In this work, we consider a new setting where both asymmetric adjacent transpositions (also known as right-shifts or left-shifts) and deletions may occur. We present several constructions of the codes correcting these errors in various cases. In particular, we design a code correcting a single deletion, $s^+$ right-shift, and $s^-$ left-shift errors with at most $(1+s)\log (n+s+1)+1$ bits of redundancy where $s=s^{+}+s^{-}$. In addition, we investigate codes correcting $t$ $0$-deletions, $s^+$ right-shift, and $s^-$ left-shift errors with both uniquely-decoding and list-decoding algorithms. Our main contribution here is the construction of a list-decodable code with list size $O(n^{\min\{s+1,t\}})$ and with at most $(\max \{t,s+1\}) \log n+O(1)$ bits of redundancy, where $s=s^{+}+s^{-}$. Finally, we construct both non-systematic and systematic codes for correcting blocks of $0$-deletions with $\ell$-limited-magnitude and $s$ adjacent transpositions

Wireless Digital Train Line for Passenger Trains \u2013 Phase 3

FR-RRD-0086-20-01-00In an extensive third phase of a Federal Railroad Administration-funded research project running from August 2020 through July 2022, a team at the Advanced Telecommunications Engineering Laboratory at the University of Nebraska-Lincoln designed, developed, and evaluated wireless communications architectures for rail services in North America, with a focus on high-speed rail services. During this phase, the team focused on mitigating a significant challenge, not only in the rail industry but in fact across all sectors: radio frequency (RF) spectrum scarcity. RF spectrum resources are a necessity for any wireless solution, and with the rapid proliferation of wireless services and applications in all aspects of daily life and society, RF resources are becoming overused and expensive to license. Therefore, the team studied RF spectrum already owned by the rail industry, but that may be abandoned, underused, or used only for legacy applications. Such bands are ideal candidates for modernization and re-use