LDPC Codes with Local and Global Decoding
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This paper presents a theoretical study of a new type of LDPC codes that is 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. In addition ,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.
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