  This paper presents a theoretical study of a new type of LDPC codes motivated
by practical storage applications. LDPCL codes (suffix L represents locality)
are LDPC codes that can be decoded either as usual over the full code block, or
locally when a smaller sub-block is accessed (to reduce latency). LDPCL codes
are designed to maximize the error-correction performance vs. rate in the usual
(global) mode, while at the same time providing a certain performance in the
local mode. We develop a theoretical framework for the design of LDPCL codes.
Our results include a design tool to construct an LDPC code with two
data-protection levels: local and global. We derive theoretical results
supporting this tool and we show how to achieve capacity with it. A trade-off
between the gap to capacity and the number of full-block accesses is studied,
and a finite-length analysis of ML decoding is performed to exemplify a
trade-off between the locality capability and the full-block error-correcting
capability.
