Systematic Transmission With Fountain Parity Checks for Erasure Channels With Stop Feedback

In this paper, we present new achievability bounds on the maximal achievable rate of variable-length stop-feedback (VLSF) codes operating over a binary erasure channel (BEC) at a fixed message size $M = 2^k$. We provide new bounds for VLSF codes with zero error, infinite decoding times and with nonzero error, finite decoding times. Both new achievability bounds are proved by constructing a new VLSF code that employs systematic transmission of the first $k$ bits followed by random linear fountain parity bits decoded with a rank decoder. For VLSF codes with infinite decoding times, our new bound outperforms the state-of-the-art result for BEC by Devassy \emph{et al.} in 2016. We also give a negative answer to the open question Devassy \emph{et al.} put forward on whether the $23.4\%$ backoff to capacity at $k = 3$ is fundamental. For VLSF codes with finite decoding times, numerical evaluations show that the achievable rate for VLSF codes with a moderate number of decoding times closely approaches that for VLSF codes with infinite decoding times.Comment: 7 pages, double column, 4 figures; comments are welcome! changes in v2: corrected 2 typos in v1. arXiv admin note: substantial text overlap with arXiv:2205.1539

High-Rate Convolutional Codes with CRC-Aided List Decoding for Short Blocklengths

Recently, rate-$1/\omega$ 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 CRCs for rate-$(\omega-1)/\omega$ 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 and the CC. Utilization of the dual trellis proposed by Yamada \emph{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 a blocklength of $128$.Comment: 6 pages; submitted to 2022 IEEE International Conference on Communications (ICC 2022

CRC-Aided High-Rate Convolutional Codes With Short Blocklengths for List Decoding

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.Comment: arXiv admin note: substantial text overlap with arXiv:2111.0792

Research progress on detection methods of N-dimethylnitrosamine in foods

N-dimethylnitrosamine is one of the most toxic nitrosamine compounds and can be produced in the process of food processing or storage. The detection methods are various with tedious operation and low accuracy. QuEChERS pretreatment combined with GC/LC-MS has been widely used in the determination of N-dimethylnitrosamine in food due to its advantages of simple operation， good extraction and purification， high sensitivity， stable recovery and effective improvement of detection rate and throughput. The pretreatment methods， detection equipment and detection parameters of N-dimethylnitrosamine in food were compared to analyze the advantages and disadvantages of different methods

Efficient Reliable Communication in the Short Blocklength Regime Through List Decoding and Through Feedback

This dissertation consists of three parts investigating the efficient reliable communication in the short blocklength regime for classical channels in three different settings: (i) no feedback, (ii) full, noiseless feedback, and (iii) finite, stop feedback. The first part focuses on the non-feedback binary-input additive white Gaussian noise (AWGN) channel. A long-standing research problem is to design good linear block codes for this channel. As its primary contribution, we propose the cyclic-redundancy-check-aided (CRC-aided) convolutional code under serial list Viterbi decoding (SLVD). To design a good CRC-aided convolutional code, we propose the distance-spectrum optimal (DSO) CRC polynomial and provide an efficient search algorithm for a given convolutional code. We then analyze the performance and complexity of the SLVD for the CRC-aided convolutional code. For transmitting 64 information bits, simulation shows that some CRC-aided convolutional codes beat the random-coding union (RCU) bound at short blocklength.The second part of the dissertation focuses on the binary asymmetric channel (BAC) with full, noiseless feedback, including the binary symmetric channel (BSC) as a special case. Building on the small-enough-difference (SED) coding scheme of Naghshvar et al. originally proposed for symmetric binary-input channels with feedback, we generalize the coding scheme to the class of BACs with feedback, and establish a non-asymptotic achievability bound for the deterministic variable-length feedback (VLF) code constructed from the generalized SED coding scheme. In the specific case of the BSC, we present a refined non-asymptotic VLF achievability bound. Despite the extreme use of feedback, Naghshvar et al.'s results on the BSC with full feedback appear to be inferior to Polyanskiy's bound for codes with a limited use of feedback, known as the variable-length stop-feedback (VLSF) codes. In contrast, numerical evaluations show that our VLF achievability bounds outperform Polyanskiy's VLSF achievability bound for both BAC and BSC cases.The third part of the dissertation focuses on the performance of VLSF codes with finite optimal decoding times for the BI-AWGN channel. We first develop tight approximations on the tail probability of length-n cumulative information density which will play an important role in numerical evaluations. Building on a recent result of Yavas et al. on VLSF codes with finite decoding times, the problem reduces to an integer program of minimizing the upper bound of average blocklength subject to the average error probability, minimum gap, and integer constraints. By allowing real-valued decoding times and using a two-step minimization, we derive the gap-constrained sequential differential optimization procedure to numerically evaluate the achievability bound. Numerical evaluations show that Polyanskiy's bound for VLSF codes, which assumes infinite decoding times, can be closely approached with a finite (and relatively small) number of decoding times

Distributed decoding of convolutional network error correction codes

A Viterbi-like decoding algorithm is proposed in this paper for generalized convolutional network error correction coding. Different from classical Viterbi algorithm, our decoding algorithm is based on minimum error weight rather than the shortest Hamming distance between received and sent sequences. Network errors may disperse or neutralize due to network transmission and convolutional network coding. Therefore, classical decoding algorithm cannot be employed any more. Source decoding was proposed by multiplying the inverse of network transmission matrix, where the inverse is hard to compute. Starting from the Maximum A Posteriori (MAP) decoding criterion, we find that it is equivalent to the minimum error weight under our model. Inspired by Viterbi algorithm, we propose a Viterbi-like decoding algorithm based on minimum error weight of combined error vectors, which can be carried out directly at sink nodes and can correct any network errors within the capability of convolutional network error correction codes (CNECC). Under certain situations, the proposed algorithm can realize the distributed decoding of CNECC.Comment: the full version of manuscript for ISIT 201