Concatenated Raptor Codes in NAND Flash Memory

Two concatenated coding schemes based on fixed-rate Raptor codes are proposed for error control in NAND flash memory. One is geared for off-line recovery of uncorrectable pages and the other is designed for page error correction during the normal read mode. Both proposed coding strategies assume hard-decision decoding of the inner code with inner decoding failure generating erasure symbols for the outer Raptor code. Raptor codes allow low-complexity decoding of very long codewords while providing capacity-approaching performance for erasure channels. For the off-line page recovery scheme, one whole NAND block forms a Raptor codeword with each inner codeword typically made up of several Raptor symbols. An efficient look-up-table strategy is devised for Raptor encoding and decoding which avoids using large buffers in the controller despite the substantial size of the Raptor code employed. The potential performance benefit of the proposed scheme is evaluated in terms of the probability of block recovery conditioned on the presence of uncorrectable pages. In the suggested page-error-correction strategy, on the other hand, a hard-decision-iterating product code is used as the inner code. The specific product code employed in this work is based on row-column concatenation with multiple intersecting bits to allow the use of longer component codes. In this setting the collection of bits captured within each intersection of the row-column codes acts as the Raptor symbol(s), and the intersections of failed row codes and column codes are declared as erasures. The error rate analysis indicates that the proposed concatenation provides a considerable performance boost relative to the existing error correcting system based on long Bose-Chauduri-Hocquenghem (BCH) codes.