A New Family of Constrained Codes with Applications in Data Storage Line codes make it possible to mitigate interference, to prevent short pulses, and to generate streams of bipolar signals with no directcurrent (DC) power content through balancing. They find application in magnetic recording (MR) devices, in Flash devices, and in optical recording devices. This paper introduces a new family of fixedlength, binary constrained codes, named lexicographicallyordered constrained codes (LOCO codes), for bipolar nonreturntozero signaling. LOCO codes are capacity achieving, the lexicographic indexing enables simple, practical encoding and decoding, and this simplicity is demonstrated through analysis of circuit complexity. Experimental results demonstrate a gain of up to 10% in rate achieved by LOCO codes with respect to practical runlengthlimited codes designed for the same purpose. Simulation results suggest that it is possible to achieve channel density gains of about 20% in MR systems by using a LOCO code to encode only the parity bits of a lowdensity paritycheck code before writing.

Convertible Codes: New Class of Codes for Efficient Conversion of Coded Data in Distributed Storage Erasure codes are typically used in largescale distributed storage systems to provide durability of data in the face of failures. In this setting, a set of k blocks to be stored is encoded using an n, k code to generate n blocks that are then stored on different storage nodes. A recent work by Kadekodi et al. Kadekodi et al., 2019 shows that the failure rate of storage devices vary significantly over time, and that changing the rate of the code (via a change in the parameters n and k) in response to such variations provides significant reduction in storage space requirement. However, the resource overhead of realizing such a change in the code rate on already encoded data in traditional codes is prohibitively  by this :124,application, in this work we first present a new framework to formalize the notion of code conversion  the process of converting data encoded with an nI, kI code into data encoded with an nF, kF code while maintaining desired decodability properties, such as the maximumdistanceseparable (MDS) property. We then introduce convertible codes, a new class of code pairs that allow for code conversions in a resourceefficient manner. For an important parameter regime (which we call the merge regime) along with the widely used linearity and MDS decodability constraint, we prove tight bounds on the number of nodes accessed during code conversion. In particular, our achievability result is an explicit construction of MDS convertible codes that are optimal for all parameter values in the merge regime albeit with a high field size. We then present explicit lowfieldsize constructions of optimal MDS convertible codes for a broad range of parameters in the merge regime. Our results thus show that it is indeed possible to achieve code conversions with significantly lesser resources as compared to the default approach of reencoding.