Decoding Flash Memory with Progressive Reads and Independent vs. Joint Encoding of Bits in a Cell

Wong, Nathan; Liang, Ethan; Wang, Haobo; Ranganathan, Sudarsan V. S.; Wesel, Richard D.

doi:10.1109/globecom38437.2019.9013896

Cited by 6 publications

(4 citation statements)

References 15 publications

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“…The presented results for joint decoding demonstrate a performance gain due to the cell-wise encoding compared to bit-interleaved coded modulation, where the bits are interleaved over all pages. A bit-interleaved coded modulation (BICM) approach similar to that in [24,25] would achieve better performance. However, such a method requires soft-input decoding and channel estimation to calculate log-likelihood ratios for the different bits depending on the estimated charge state.…”

Section: Discussionmentioning

confidence: 99%

“…On the other hand, the dependencies between the different bits stored in a cell can be exploited with cell-wise read operations. For instance, a method that improves the decoding performance of LDPC codes with cell-wise reading was presented in [24,25]. This method calculates log-likelihood ratios for the different bits depending on the estimated charge state.…”

Section: Introductionmentioning

confidence: 99%

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Error Correction for TLC and QLC NAND Flash Memories Using Cell-Wise Encoding

2022

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The growing error rates of triple-level cell (TLC) and quadruple-level cell (QLC) NAND flash memories have led to the application of error correction coding with soft-input decoding techniques in flash-based storage systems. Typically, flash memory is organized in pages where the individual bits per cell are assigned to different pages and different codewords of the error-correcting code. This page-wise encoding minimizes the read latency with hard-input decoding. To increase the decoding capability, soft-input decoding is used eventually due to the aging of the cells. This soft-decoding requires multiple read operations. Hence, the soft-read operations reduce the achievable throughput, and increase the read latency and power consumption. In this work, we investigate a different encoding and decoding approach that improves the error correction performance without increasing the number of reference voltages. We consider TLC and QLC flashes where all bits are jointly encoded using a Gray labeling. This cell-wise encoding improves the achievable channel capacity compared with independent page-wise encoding. Errors with cell-wise read operations typically result in a single erroneous bit per cell. We present a coding approach based on generalized concatenated codes that utilizes this property.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Error Correction for TLC and QLC NAND Flash Memories Using Cell-Wise Encoding

2022

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“…Based on Lemma 3 in [11], any binary-input discrete memoryless channel that satisfies (6) has an optimal b-bit quantizer that is determined by 2 b − 1 boundaries, which can be identified by their corresponding index values. Denote the 2 b −1 index thresholds by {ξ 1 , ξ 2 , ..., ξ 2 b −1 } ⊂ W. Unlike the dynamic programming algorithm [11], which optimizes boundaries jointly, HDQ sequentially finds thresholds according to bit level, similar to the progressive quantization in [27].…”

Section: B the Hdq Algorithmmentioning

confidence: 99%

A Reconstruction-Computation-Quantization (RCQ) Approach to Node Operations in LDPC Decoding

Wang¹,

Wesel²,

Stark

et al. 2020

GLOBECOM 2020 - 2020 IEEE Global Communications Conference

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This paper uses the reconstruction-computation-quantization (RCQ) paradigm to decode low-density parity-check (LDPC) codes. RCQ facilitates dynamic non-uniform quantization to achieve good frame error rate (FER) performance with very low message precision. For message-passing according to a flooding schedule, the RCQ parameters are designed by discrete density evolution (DDE). Simulation results on an IEEE 802.11 LDPC code show that for 4-bit messages, a flooding MinSum RCQ decoder outperforms table-lookup approaches such as information bottleneck (IB) or Min-IB decoding, with significantly fewer parameters to be stored.

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“…Note that a 1 and a 3 are independently optimized, it is easy to show that the solution of a 1 is independent to the solution of a 3 . A similar idea is also used in optimizing progressive reads for flash memory cells [13].We borrow the metric of Information Bottleneck algorithm and develop a sequential threshold searching algorithm (STS) to find a i . Given a l and a r , r > l and starting from a l+1 , STS sequentially calculates the merging costs that a i is merged into left or right cluster until left merging cost is larger than right merging cost.…”

Section: Hierarchical Dynamic Quantizationmentioning

confidence: 99%

A Reconstruction-Computation-Quantization (RCQ) Approach to Node Operations in LDPC Decoding

Wang

Stark

Wesel

et al. 2020

Preprint

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In this paper, we propose a finite-precision decoding method that features the three steps of Reconstruction, Computation, and Quantization (RCQ). Unlike Mutual-Information-Maximization Quantized Belief Propagation (MIM-QBP), RCQ can approximate either belief propagation or Min-Sum decoding. One problem faced by MIM-QBP decoder is that it cannot work well when the fraction of degree-2 variable nodes is large. However, sometimes a large fraction of degree-2 variable nodes is necessary for a fast encoding structure, as seen in the IEEE 802.11 standard and the DVB-S2 standard. In contrast, the proposed RCQ decoder may be applied to any off-the-shelf LDPC code, including those with a large fraction of degree-2 variable nodes. Our simulations show that a 4-bit Min-Sum RCQ decoder delivers frame error rate (FER) performance around 0.1dB of full-precision belief propagation (BP) for the IEEE 802.11 standard LDPC code in the low SNR region. The RCQ decoder actually outperforms full-precision BP in the high SNR region because it overcomes elementary trapping sets that create an error floor under BP decoding. This paper also introduces Hierarchical Dynamic Quantization (HDQ) to design the non-uniform quantizers required by RCQ decoders. HDQ is a low-complexity design technique that is slightly sub-optimal. Simulation results comparing HDQ and an optimal quantizer on the symmetric binary-input memoryless additive white Gaussian noise channel show a loss in mutual information between these two quantizers of less than 10 −6 bits, which is negligible for practical applications.

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Decoding Flash Memory with Progressive Reads and Independent vs. Joint Encoding of Bits in a Cell

Cited by 6 publications

References 15 publications

Error Correction for TLC and QLC NAND Flash Memories Using Cell-Wise Encoding

Error Correction for TLC and QLC NAND Flash Memories Using Cell-Wise Encoding

A Reconstruction-Computation-Quantization (RCQ) Approach to Node Operations in LDPC Decoding

A Reconstruction-Computation-Quantization (RCQ) Approach to Node Operations in LDPC Decoding

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