Tsung-Yi Chen

Enhanced Precision Through Multiple Reads for LDPC Decoding in Flash Memories

Multiple reads of the same Flash memory cell with distinct word-line voltages provide enhanced precision for LDPC decoding. In this paper, the word-line voltages are optimized by maximizing the mutual information (MI) of the quantized channel. The enhanced precision from a few additional reads allows frame error rate (FER) performance to approach that of full-precision soft information and enables an LDPC code to significantly outperform a BCH code. A constant-ratio constraint provides a significant simplification in the optimization with no noticeable loss in performance. For a well-designed LDPC code, the quantization that maximizes the mutual information also minimizes the FER in our simulations. However, for an example LDPC code with a high error floor caused by small absorbing sets, the MMI quantization does not provide the lowest frame error rate. The best quantization in this case introduces more erasures than would be optimal for the channel MI in order to mitigate the absorbing sets of the poorly designed code. The paper also identifies a trade-off in LDPC code design when decoding is performed with multiple precision levels; the best code at one level of precision will typically not be the best code at a different level of precision.

Protograph-Based Raptor-Like LDPC Codes

This paper proposes protograph-based Raptor-like (PBRL) codes as a class of rate-compatible low-density parity-check codes for binary-input AWGN channels. As with the Raptor codes, exclusive-OR operations on precoded bits produce additional parity bits providing extensive rate compatibility. Unlike Raptor codes, each additional parity bit in the protograph is explicitly designed to optimize the density evolution threshold. During the lifting process, approximate cycle extrinsic message degree (ACE) and circulant progressive edge growth (CPEG) constraints are used to avoid undesirable graphical structures. Some density-evolution performance is sacrificed to obtain lower error floors, particularly at short block-lengths. Simulation results are shown for information block sizes of k = 1032 and 16 384. For a target frame error rate of 10-5, at each rate, the k = 1032 and 16 384 code families perform within 1 dB and 0.4 dB of both the Gallager bound and the normal approximation, respectively. The 16 384 code family outperforms the best known standardized code family, namely, the AR4JA codes. The PBRL codes also outperform DVB-S2 codes that have the advantages of longer blocklengths and outer BCH codes. Performance is similar to RC code families designed by Nguyen et al. that do not constrain codes to have the PBRL structure and involve simulation in the optimization process at each rate.

Protograph-Based Raptor-Like LDPC Codes for Rate Compatibility with Short Blocklengths

This paper presents a new class of rate-compatible LDPC codes, protograph-based Raptor-like (PBRL) codes. The proposed PBRL codes are jointly decodable with an iterative belief propagation decoder. As with Raptor codes, additional parity bits can be easily produced by exclusive-or operations on the precoded bits, providing extensive rate compatibility. This paper provides a design procedure that optimizes this class of rate- compatible LDPC codes. The new PBRL codes outperform 3GPP rate-compatible turbo codes with the same short blocklength at high SNR and show no sign of an error floor at the FER region of

Protograph-based Raptor-like LDPC codes with low thresholds

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A rate-compatible sphere-packing analysis of feedback coding with limited retransmissions

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Variable-Length Convolutional Coding for Short Blocklengths With Decision Feedback

This paper presents a new construction of punctured-node protograph-based Raptor-like (PN-PBRL) codes that is suitable for long-blocklength applications. As with the Raptor codes, additional parity bits can be easily produced by exclusive-OR operations on the precoded bits, providing extensive rate compatibility. The new construction provides low iterative decoding thresholds that are within 0.45 dB of the capacity for all code rates studied, and the construction is suitable for long blocklengths. Comparing at the same information block size of k = 16368 bits, the PN-PBRL codes are as good as the best known AR4JA codes in the waterfall region. The PN-PBRL codes also perform comparably to DVB-S2 LDPC codes even though the DVBi-S2 codes have longer blocklength and outer BCH codes.

Increasing flash memory lifetime by dynamic voltage allocation for constant mutual information

Recent work by Polyanskiy et al. and Chen et al. has excited new interest in using feedback to approach capacity with low latency. Polyanskiy showed that feedback identifying the first symbol at which decoding is successful allows capacity to be approached with surprisingly low latency. This paper uses Chens rate-compatible sphere-packing (RCSP) analysis to study what happens when symbols must be transmitted in packets, as with a traditional hybrid ARQ system, and limited to relatively few (six or fewer) incremental transmissions. Numerical optimizations find the series of progressively growing cumulative block lengths that enable RCSP to approach capacity with the minimum possible latency. RCSP analysis shows that five incremental transmissions are sufficient to achieve 92% of capacity with an average block length of fewer than 101 symbols on the AWGN channel with SNR of 2.0 dB. The RCSP analysis provides a decoding error trajectory that specifies the decoding error rate for each cumulative block length. Though RCSP is an idealization, an example tail-biting convolutional code matches the RCSP decoding error trajectory and achieves 91% of capacity with an average block length of 102 symbols on the AWGN channel with SNR of 2.0 dB. We also show how RCSP analysis can be used in cases where packets have deadlines associated with them (leading to an outage probability).

Reliability-based error detection for feedback communication with low latency

This paper presents a variable-length decision-feedback coding scheme that achieves high rates at short blocklengths. This scheme uses the reliability-output Viterbi algorithm (ROVA) to determine when the receivers decoding estimate satisfies a given error constraint. We evaluate the performance of both terminated and tail-biting convolutional codes at average blocklengths less than 300 symbols, using the ROVA and the tail-biting ROVA, respectively. Comparing with recent results from finite-blocklength information theory, simulations for both the BSC and the AWGN channel show that the reliability-based decision-feedback scheme can surpass the random-coding lower bound on throughput for feedback codes at some blocklengths less than 100 symbols. This is true both when decoding after every symbol is permitted and when decoding is limited to a small number of increments. Finally, the performance of the reliability-based stopping rule with the ROVA is compared with retransmission decisions based on CRCs. For short blocklengths where the latency overhead of the CRC bits is severe, the ROVA-based approach delivers superior rates.

Histogram-based Flash channel estimation

The read channel in Flash memory systems degrades over time because the Fowler-Nordheim tunneling used to apply charge to the floating gate eventually compromises the integrity of the cell because of tunnel oxide degradation. While degradation is commonly measured in the number of program/erase cycles experienced by a cell, the degradation is proportional to the number of electrons forced into the floating gate and later released by the erasing process. By managing the amount of charge written to the floating gate to maintain a constant read-channel mutual information, Flash lifetime can be extended. This paper proposes an overall system approach based on information theory to extend the lifetime of a flash memory device. Using the instantaneous storage capacity of a noisy flash memory channel, our approach allocates the read voltage of flash cell dynamically as it wears out gradually over time. A practical estimation of the instantaneous capacity is also proposed based on soft information via multiple reads of the memory cells.

A Sphere-Packing Analysis of Incremental Redundancy with Feedback

This paper presents a reliability-based decoding scheme for variable-length coding with feedback and demonstrates via simulation that it can achieve higher rates than Polyanskiy et al.s random coding lower bound for variable-length feedback (VLF) coding on both the BSC and AWGN channel. The proposed scheme uses the reliability output Viterbi algorithm (ROVA) to compute the word error probability after each decoding attempt, which is compared against a target error threshold and used as a stopping criterion to terminate transmission. The only feedback required is a single bit for each decoding attempt, informing the transmitter whether the ROVA-computed word-error probability is sufficiently low. Furthermore, the ROVA determines whether transmission/decoding may be terminated without the need for a rate-reducing CRC.