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1. Channel coding at low capacity

   Fereydounian, Mohammad; Hassani, Hamed; Jamal, Vahid; Mahdavifar, Hessam (August 2023, IEEE journal on selected areas in information theory)

   Low-capacity scenarios have become increasingly important in the technology of the In- ternet of Things (IoT) and the next generation of wireless networks. Such scenarios require efficient and reliable transmission over channels with an extremely small capacity. Within these constraints, the state-of-the-art coding techniques may not be directly applicable. More- over, the prior work on the finite-length analysis of optimal channel coding provides inaccurate predictions of the limits in the low-capacity regime. In this paper, we study channel coding at low capacity from two perspectives: fundamental limits at finite length and code construc- tions. We first specify what a low-capacity regime means. We then characterize finite-length fundamental limits of channel coding in the low-capacity regime for various types of channels, including binary erasure channels (BECs), binary symmetric channels (BSCs), and additive white Gaussian noise (AWGN) channels. From the code construction perspective, we charac- terize the optimal number of repetitions for transmission over binary memoryless symmetric (BMS) channels, in terms of the code blocklength and the underlying channel capacity, such that the capacity loss due to the repetition is negligible. Furthermore, it is shown that capacity- achieving polar codes naturally adopt the aforementioned optimal number of repetitions. 

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2. Coded Distributed Computing: Performance Limits and Code Designs

   https://doi.org/10.1109/ITW44776.2019.8989097  

   Jamali, Mohammad Vahid; Soleymani, Mahdi; Mahdavifar, Hessam (August 2019, 2019 IEEE Information Theory Workshop (ITW))

   We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $$k$$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $$n$$ distributed nodes. The goal is to reduce the average execution time of the computational job. We provide a connection between the problem of characterizing the average execution time of a coded distributed computing system and the problem of analyzing the error probability of codes of length $$n$$ used over erasure channels. Accordingly, we present closed-form expressions for the execution time using binary random linear codes and the best execution time any linear-coded distributed computing system can achieve. It is also shown that there exist good binary linear codes that attain, asymptotically, the best performance any linear code, not necessarily binary, can achieve. We also investigate the performance of coded distributed computing systems using polar and Reed-Muller (RM) codes that can benefit from low-complexity decoding, and superior performance, respectively, as well as explicit constructions. The proposed framework in this paper can enable efficient designs of distributed computing systems given the rich literature in the channel coding theory. 

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3. Efficiently Computable Converses for Finite-Blocklength Communication

   https://doi.org/10.1109/ISIT50566.2022.9834427  

   Areces, Felipe; Song, Dan; Wesel, Richard; Wagner, Aaron B. (June 2022, 2022 IEEE International Symposium on Information Theory (ISIT))

   This paper presents a method for computing a finite-blocklength converse for the rate of fixed-length codes with feedback used on discrete memoryless channels (DMCs). The new converse is expressed in terms of a stochastic control problem whose solution can be efficiently computed using dynamic programming and Fourier methods. For channels such as the binary symmetric channel (BSC) and binary erasure channel (BEC), the accuracy of the proposed converse is similar to that of existing special-purpose converse bounds, but the new converse technique can be applied to arbitrary DMCs. We provide example applications of the new converse technique to the binary asymmetric channel (BAC) and the quantized amplitude-constrained AWGN channel. 

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

   https://doi.org/10.1109/ISIT57864.2024.10619630  

   Yang, Hengjie; Wesel, Richard D (July 2024, IEEE)

   This paper presents 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 bounds for two cases: The first case considers VLSF codes with possibly infinite decoding times and zero error probability. The second case limits the maximum (finite) number of decoding times and specifies a maximum tolerable probability of error. Both new achievability bounds are proved by constructing a new VLSF code that employs systematic transmission of the first k message 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 et al. in 2016. We show that the backoff from capacity reduces to zero as the erasure probability decreases, thus giving a negative answer to the open question Devassy et al. posed on whether the 23.4% backoff to capacity at k=3 is fundamental to all BECs. For VLSF codes with finite decoding times, numerical evaluations show that the systematic transmission followed by random linear fountain coding performs better than random linear coding in terms of achievable rates. 

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5. Random Linear Streaming Codes in the Finite Memory Length and Decoding Deadline Regime

   https://doi.org/10.1109/ISIT45174.2021.9518162  

   Su, Pin-Wen; Huang, Yu-Chih; Lin, Shih-Chun; Wang, I-Hsiang; Wang, Chih-Chun (July 2021, 2021 IEEE International Symposium on Information Theory (ISIT))

   Streaming codes take a string of source symbols as input and output a string of coded symbols in real time, which effectively eliminate the queueing delay and are regarded as a promising scheme for low latency communications. Aiming at quantifying the fundamental latency performance of random linear streaming codes (RLSCs) over i.i.d. symbol erasure channels, this work derives the exact error probability under, simultaneously, the finite memory length and finite decoding deadline constraints. The result is then used to examine the tradeoff among memory length (complexity), decoding deadline (delay), and error probability (reliability) of RLSCs for the first time in the literature. Two critical observations are made: (i) Too much memory can adversely impact the performance under a finite decoding deadline constraint, a surprising finding not captured by the traditional wisdom that large memory length monotonically improves the performance in the asymptotic regime; (ii) The end-to-end delay of the RLSC is roughly 50% of that of the MDS block code when under identical code rate and error probability requirements. This implies that switching from block codes to RLSCs not only eliminates the queueing delay (thus 50%) but also has little negative impact on the error probability. 

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