We study spatially coupled LDPC codes that allow access to sub-blocks much smaller than the full code block. Sub-block access is realized by a semi-global decoder that decodes a chosen target sub-block by only accessing the target, plus a prescribed number of helper sub-blocks adjacent in the code chain. This paper develops a theoretical methodology for analyzing the semi-global decoding performance of spatially coupled LDPC codes constructed from protographs. The main result shows that semi-global decoding thresholds can be derived from certain thresholds we define for the single-sub-block graph. These characterizing thresholds are also used for deriving lower bounds on the decoder’s performance over channels with variability across sub-blocks, which are motivated by applications in data storage.

A new type of spatially coupled low-density parity-check (SC-LDPC) codes motivated by practical storage applications is presented. SC-LDPCL codes (suffix `L' stands for locality) can be decoded locally at the level of sub-blocks that are much smaller than the full code block, thus offering flexible access to the coded information alongside the strong reliability of the global full-block decoding. Toward that, we propose constructions of SC-LDPCL codes that allow controlling the trade-off between local and global correction performance. In addition to local and global decoding, the paper develops a density-evolution analysis for a decoding mode we call semi-global decoding, in which the decoder has access to the requested sub-block plus a prescribed number of sub-blocks around it. SC-LDPCL codes are also studied under a channel model with variability across sub-blocks, for which decoding-performance lower bounds are derived.

A new approach for designing bilayer and multi-layer LDPC codes is proposed and studied in the asymptotic regime. The ensembles are defined through individual uni-variate degree distributions, one for each layer. We present a construction that: 1) enables low-complexity decoding for high-SNR channel instances, 2) provably approaches capacity for low-SNR instances, 3) scales linearly (in terms of design complexity) in the number of layers. For the setup where decoding the second layer is significantly more costly than the first layer, we propose an optimal-cost decoding schedule and study the trade-off between code rate and decoding cost.

SC-LDPC codes with sub-block locality can be decoded locally at the level of sub-blocks that are much smaller than the full code block, thus providing fast access to the coded information. The same code can also be decoded globally using the entire code block, for increased data reliability. In this paper, we pursue the analysis and design of such codes from both finite-length and asymptotic lenses. This mixed approach has rarely been applied in designing SC codes, but it is beneficial for optimizing code graphs for local and global performance simultaneously. Our proposed framework consists of two steps: 1) designing the local code for both threshold and cycle counts, and 2) designing the coupling of local codes for the best cycle count in the global design.

We study a new decoding strategy of multi-block SC-LDPC codes motivated by data-storage applications. To decode a sub-block out of the full code block, our proposed decoder accesses a small number of sub-blocks around the desired sub-block. We call this decoding strategy "semi-global decoding", and parametrize it by its access cost: the number of accessed sub-blocks. We provide a theoretical characterization of decoding performance, and evaluate this performance for random-access SC-LDPC ensembles.

This paper presents a theoretical study of a new type of LDPC codes that is highly 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 over the binary erasure channel. Our results include generalizing the density-evolution analysis to two dimensions, proving the existence of a decoding threshold and showing how to compute it, and constructing capacity-achieving sequences for any pair of local and global thresholds. Proofs and more results are made available at the arXiv (http://arxiv.org/abs/1801.03951).

This paper gives improved Rényi entropy power inequalities (R-EPIs). Consider a sum Sn= Σk=1nXkof n independent continuous random vectors taking values on ℝd, and let α ∈ [1, ∞]. An R-EPI provides a lower bound on the order-α Rényi entropy power of Snthat, up to a multiplicative constant (which may depend in general on n, α, d), is equal to the sum of the order-α Rényi entropy powers of the n random vectors {Xk}k=1n. For α = 1, the R-EPI coincides with the wellknown entropy power inequality by Shannon. The first improved R-EPI is obtained by tightening the recent R-EPI by Bobkov and Chistyakov, which relies on the sharpened Young's inequality. A further improvement of the R-EPI also relies on convex optimization and results on rank-one modification of a real-valued diagonal matrix.