For a two-variance model of the Flash read channel that degrades as a function of the number of program/erase cycles, this paper demonstrates that selecting write voltages to maximize the minimum page mutual information (MI) can increase device lifetime. In multi-level cell (MLC) Flash memory, one of four voltage levels is written to each cell, according to the values of the most-significant bit (MSB) page and the least-significant bit (LSB) page. In our model, each voltage level is then distorted by signal-dependent additive Gaussian noise that approximates the Flash read channel. When performing an initial read of a page in MLC flash, one (for LSB) or two (for MSB) bits of information are read for each cell of the page. If LDPC decoding fails after the initial read, then an enhanced-precision read is performed. This paper shows that jointly designing write voltage levels and read thresholds to maximize the minimum MI between a page and its associated initial or enhanced-precision read bits can improve LDPC decoding performance.

Recently, rate-$1/n$zero-terminated (ZT) and tail-biting (TB) convolutional codes (CCs) with cyclic redundancy check (CRC)-aided list decoding have been shown to closely approach the random-coding union (RCU) bound for short blocklengths. This paper designs CRC polynomials for rate-$(n-1)/n$ZT and TB CCs with short blocklengths. This paper considers both standard rate-$(n-1)/n$CC polynomials and rate-$(n-1)/n$designs resulting from puncturing a rate-$1/2$code. The CRC polynomials are chosen to maximize the minimum distance$d_{\min }$and minimize the number of nearest neighbors$A_{d_{\min }}$. For the standard rate-$(n-1)/n$codes, utilization of the dual trellis proposed by Yamada et al. lowers the complexity of CRC-aided serial list Viterbi decoding (SLVD). CRC-aided SLVD of the TBCCs closely approaches the RCU bound at a blocklength of 128. This paper compares the FER performance (gap to the RCU bound) and complexity of the CRC-aided standard and punctured ZTCCs and TBCCs. This paper also explores the complexity-performance trade-off for three TBCC decoders: a single-trellis approach, a multi-trellis approach, and a modified single-trellis approach with pre-processing using the wrap around Viterbi algorithm.

Recently, rate-1/ω zero-terminated and tail-biting convolutional codes (ZTCCs and TBCCs) with cyclic-redundancy-check (CRC)-aided list decoding have been shown to closely approach the random-coding union (RCU) bound for short blocklengths. This paper designs CRC polynomials for rate-(ω – 1)/ω CCs with short blocklengths, considering both the ZT and TB cases. The CRC design seeks to optimize the frame error rate (FER) performance of the code resulting from the concatenation of the CRC code and the CC. Utilization of the dual trellis proposed by Yamada et al. lowers the complexity of CRC-aided serial list Viterbi decoding (SLVD) of ZTCCs and TBCCs. CRC-aided SLVD of the TBCCs closely approaches the RCU bound at blocklength of 128.