We consider the concatenation of a convolutional code (CC) with an optimized cyclic redundancy check (CRC) code as a promising paradigm for good short blocklength codes. The resulting CRC-aided convolutional code naturally permits the use of serial list Viterbi decoding (SLVD) to achieve maximum-likelihood decoding. The convolutional encoder of interest is of rate-$1/\omega $and the convolutional code is either zero-terminated (ZT) or tail-biting (TB). The resulting CRC-aided convolutional code is called a CRC-ZTCC or a CRC-TBCC. To design a good CRC-aided convolutional code, we propose thedistance-spectrum optimal (DSO)CRC polynomial. A DSO CRC search algorithm for the TBCC is provided. Our analysis reveals that the complexity of SLVD is governed by the expected list rank which converges to 1 at high SNR. This allows a good performance to be achieved with a small increase in complexity. In this paper, we focus on transmitting 64 information bits with a rate-1/2 convolutional encoder. For a target error probability$10^{-4}$, simulations show that the best CRC-ZTCC approaches the random-coding union (RCU) bound within 0.4 dB. Several CRC-TBCCs outperform the RCU bound at moderate SNR values.

This paper uses convolutional codes (CCs) with distance-spectrum optimal (DSO) cyclic redundancy checks (CRCs) and the serial list Viterbi algorithm (S-LVA) to approach the random coding union (RCU) bound with low decoding complexity at the target FER. We show, for example, that a 64-state zero-terminated CC with a DSO CRC can achieve performance within 0.5 dB of the RCU bound for information blocklength k=64 at FER of 10-3. We also show that a tail-biting CC with a DSO CRC can achieve even better performance, within 0.05 dB of the RCU bound at FER of 10-4for a 256-state CC with k=64. This paper provides analysis of decoding complexity, which for S-LVA depends on the expected list size. We show that if the target FER is low enough, the expected list size approaches one so that the average complexity of S-LVA approaches that of standard soft Viterbi on the CC, i.e., with no list decoding. We also provide DSO CRCs for CCs with k=64 and rates of 1/2, 1/3, 1/6 and 1/12 for the 5G new radio control channel and compare their performance with polar codes.

This paper develops a paradigm for optimizing progressive reads for flash memory cells that maximize the conditional mutual information (MI) given previous reads and shows that some progressive reads provide substantially more MI than others. We study two flash storage techniques: 1) the common practice of independently encoding each bit of a cell into a separate codeword and 2) jointly encoding all the bits in the cell into the same codeword. We quantify the MI gap between joint and independent encoding and show that this gap becomes negligible when progressive reads are available. The paper provides LDPC simulations that confirm the MI analysis.

This paper provides a reduced-complexity approach to maximum likelihood (ML) decoding of cyclic codes. A cyclic code with generator polynomial gcyclic(x) may be considered a terminated convolutional code with a nominal rate of 1. The trellis termination redundancy lowers the rate from 1 to the actual rate of the cyclic code. The proposed decoder represents gcyclic(x) as the product of two polynomials, a convolutional code (CC) polynomial gcc(x) and a cyclic redundancy check (CRC) polynomial gcrc(x), i.e., gcyclic(x) = gcc(x)gcrc(x). This representation facilitates serial list Viterbi algorithm (S-LVA) decoding. Viterbi decoding is performed on the natural trellis for gcc(x), and gcrc(x) is used as a CRC to determine when the S-LVA should conclude. At typical target frame error rates, the expected list size of S-LVA is small, and the average decoding complexity is dominated by the trellis complexity of gcc(x) rather than gcyclic(x). Some high-rate binary Bose-Chaudhuri- Hocquenghem (BCH) examples show that the proposed use of S-LVA via factorization significantly lowers complexity as compared to using the minimum-complexity trellis representation of gcyclic(x) for soft ML decoding.