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<button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2412.20771">arXiv:2412.20771</a> <span> [<a href="https://arxiv.org/pdf/2412.20771">pdf</a>, <a href="https://arxiv.org/ps/2412.20771">ps</a>, <a href="https://arxiv.org/format/2412.20771">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Information Theory">cs.IT</span> </div> </div> <p class="title is-5 mathjax"> Optimally Decoding Two-Dimensional Reed-Solomon Codes up to the Half-Singleton Bound </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Singhvi%2C+S">Shubhransh Singhvi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2412.20771v1-abstract-short" style="display: inline;"> Constructing Reed-Solomon (RS) codes capable of correcting insertion and deletion errors (ins-del errors) has been the focus of numerous recent studies. However, the development of efficient decoding algorithms for such RS codes has not garnered significant attention and remains an important and intriguing open problem. In this work, we take a first step toward addressing this problem by designing… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.20771v1-abstract-full').style.display = 'inline'; document.getElementById('2412.20771v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2412.20771v1-abstract-full" style="display: none;"> Constructing Reed-Solomon (RS) codes capable of correcting insertion and deletion errors (ins-del errors) has been the focus of numerous recent studies. However, the development of efficient decoding algorithms for such RS codes has not garnered significant attention and remains an important and intriguing open problem. In this work, we take a first step toward addressing this problem by designing an optimal-time decoding algorithm for the special case of two-dimensional RS codes, capable of decoding up to the half-Singleton bound. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2412.20771v1-abstract-full').style.display = 'none'; document.getElementById('2412.20771v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 December, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2407.10026">arXiv:2407.10026</a> <span> [<a href="https://arxiv.org/pdf/2407.10026">pdf</a>, <a href="https://arxiv.org/format/2407.10026">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Information Theory">cs.IT</span> </div> </div> <p class="title is-5 mathjax"> Conditional Entropies of k-Deletion/Insertion Channels </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Singhvi%2C+S">Shubhransh Singhvi</a>, <a href="/search/cs?searchtype=author&query=Sabary%2C+O">Omer Sabary</a>, <a href="/search/cs?searchtype=author&query=Bar-Lev%2C+D">Daniella Bar-Lev</a>, <a href="/search/cs?searchtype=author&query=Yaakobi%2C+E">Eitan Yaakobi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2407.10026v1-abstract-short" style="display: inline;"> The channel output entropy of a transmitted sequence is the entropy of the possible channel outputs and similarly the channel input entropy of a received sequence is the entropy of all possible transmitted sequences. The goal of this work is to study these entropy values for the k-deletion, k-insertion channels, where exactly k symbols are deleted, inserted in the transmitted sequence, respectivel… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.10026v1-abstract-full').style.display = 'inline'; document.getElementById('2407.10026v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2407.10026v1-abstract-full" style="display: none;"> The channel output entropy of a transmitted sequence is the entropy of the possible channel outputs and similarly the channel input entropy of a received sequence is the entropy of all possible transmitted sequences. The goal of this work is to study these entropy values for the k-deletion, k-insertion channels, where exactly k symbols are deleted, inserted in the transmitted sequence, respectively. If all possible sequences are transmitted with the same probability then studying the input and output entropies is equivalent. For both the 1-deletion and 1-insertion channels, it is proved that among all sequences with a fixed number of runs, the input entropy is minimized for sequences with a skewed distribution of their run lengths and it is maximized for sequences with a balanced distribution of their run lengths. Among our results, we establish a conjecture by Atashpendar et al. which claims that for the 1-deletion channel, the input entropy is maximized by the alternating sequences over all binary sequences. This conjecture is also verified for the 2-deletion channel, where it is proved that constant sequences with a single run minimize the input entropy. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.10026v1-abstract-full').style.display = 'none'; document.getElementById('2407.10026v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">arXiv admin note: substantial text overlap with arXiv:2202.03024</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2405.02705">arXiv:2405.02705</a> <span> [<a href="https://arxiv.org/pdf/2405.02705">pdf</a>, <a href="https://arxiv.org/format/2405.02705">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Information Theory">cs.IT</span> </div> </div> <p class="title is-5 mathjax"> Peak Age of Information under Tandem of Queues </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Sinha%2C+A">Ashirwad Sinha</a>, <a href="/search/cs?searchtype=author&query=Singhvi%2C+S">Shubhransh Singhvi</a>, <a href="/search/cs?searchtype=author&query=Mankar%2C+P+D">Praful D. Mankar</a>, <a href="/search/cs?searchtype=author&query=Dhillon%2C+H+S">Harpreet S. Dhillon</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2405.02705v1-abstract-short" style="display: inline;"> This paper considers a communication system where a source sends time-sensitive information to its destination via queues in tandem. We assume that the arrival process as well as the service process (of each server) are memoryless, and each of the servers has no buffer. For this setup, we develop a recursive framework to characterize the mean peak age of information (PAoI) under preemptive and non… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.02705v1-abstract-full').style.display = 'inline'; document.getElementById('2405.02705v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2405.02705v1-abstract-full" style="display: none;"> This paper considers a communication system where a source sends time-sensitive information to its destination via queues in tandem. We assume that the arrival process as well as the service process (of each server) are memoryless, and each of the servers has no buffer. For this setup, we develop a recursive framework to characterize the mean peak age of information (PAoI) under preemptive and non-preemptive policies with $N$ servers having different service rates. For the preemptive case, the proposed framework also allows to obtain mean age of information (AoI). <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.02705v1-abstract-full').style.display = 'none'; document.getElementById('2405.02705v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 May, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Accepted at IEEE ISIT'24</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2403.15827">arXiv:2403.15827</a> <span> [<a href="https://arxiv.org/pdf/2403.15827">pdf</a>, <a href="https://arxiv.org/ps/2403.15827">ps</a>, <a href="https://arxiv.org/format/2403.15827">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Information Theory">cs.IT</span> </div> </div> <p class="title is-5 mathjax"> Permutation Recovery Problem against Deletion Errors for DNA Data Storage </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Singhvi%2C+S">Shubhransh Singhvi</a>, <a href="/search/cs?searchtype=author&query=Gupta%2C+C">Charchit Gupta</a>, <a href="/search/cs?searchtype=author&query=Boruchovsky%2C+A">Avital Boruchovsky</a>, <a href="/search/cs?searchtype=author&query=Goldberg%2C+Y">Yuval Goldberg</a>, <a href="/search/cs?searchtype=author&query=Kiah%2C+H+M">Han Mao Kiah</a>, <a href="/search/cs?searchtype=author&query=Yaakobi%2C+E">Eitan Yaakobi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2403.15827v1-abstract-short" style="display: inline;"> Owing to its immense storage density and durability, DNA has emerged as a promising storage medium. However, due to technological constraints, data can only be written onto many short DNA molecules called data blocks that are stored in an unordered way. To handle the unordered nature of DNA data storage systems, a unique address is typically prepended to each data block to form a DNA strand. Howev… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.15827v1-abstract-full').style.display = 'inline'; document.getElementById('2403.15827v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2403.15827v1-abstract-full" style="display: none;"> Owing to its immense storage density and durability, DNA has emerged as a promising storage medium. However, due to technological constraints, data can only be written onto many short DNA molecules called data blocks that are stored in an unordered way. To handle the unordered nature of DNA data storage systems, a unique address is typically prepended to each data block to form a DNA strand. However, DNA storage systems are prone to errors and generate multiple noisy copies of each strand called DNA reads. Thus, we study the permutation recovery problem against deletions errors for DNA data storage. The permutation recovery problem for DNA data storage requires one to reconstruct the addresses or in other words to uniquely identify the noisy reads. By successfully reconstructing the addresses, one can essentially determine the correct order of the data blocks, effectively solving the clustering problem. We first show that we can almost surely identify all the noisy reads under certain mild assumptions. We then propose a permutation recovery procedure and analyze its complexity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.15827v1-abstract-full').style.display = 'none'; document.getElementById('2403.15827v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 March, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">arXiv admin note: substantial text overlap with arXiv:2305.04597</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2403.07754">arXiv:2403.07754</a> <span> [<a href="https://arxiv.org/pdf/2403.07754">pdf</a>, <a href="https://arxiv.org/format/2403.07754">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Information Theory">cs.IT</span> </div> </div> <p class="title is-5 mathjax"> An Optimal Sequence Reconstruction Algorithm for Reed-Solomon Codes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Singhvi%2C+S">Shubhransh Singhvi</a>, <a href="/search/cs?searchtype=author&query=Con%2C+R">Roni Con</a>, <a href="/search/cs?searchtype=author&query=Kiah%2C+H+M">Han Mao Kiah</a>, <a href="/search/cs?searchtype=author&query=Yaakobi%2C+E">Eitan Yaakobi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2403.07754v1-abstract-short" style="display: inline;"> The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a scenario where the sender transmits a codeword from some codebook, and the receiver obtains $N$ noisy outputs of the codeword. We study the problem of efficient reconstruction using $N$ outputs that are each corrupted by at most $t$ substitutions. Specifically, for the ubiquitous Reed-Solomon codes, we adapt the Ko… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.07754v1-abstract-full').style.display = 'inline'; document.getElementById('2403.07754v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2403.07754v1-abstract-full" style="display: none;"> The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a scenario where the sender transmits a codeword from some codebook, and the receiver obtains $N$ noisy outputs of the codeword. We study the problem of efficient reconstruction using $N$ outputs that are each corrupted by at most $t$ substitutions. Specifically, for the ubiquitous Reed-Solomon codes, we adapt the Koetter-Vardy soft-decoding algorithm, presenting a reconstruction algorithm capable of correcting beyond Johnson radius. Furthermore, the algorithm uses $\mathcal{O}(nN)$ field operations, where $n$ is the codeword length. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.07754v1-abstract-full').style.display = 'none'; document.getElementById('2403.07754v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 March, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Submitted to IEEE ISIT 2024</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2305.04597">arXiv:2305.04597</a> <span> [<a href="https://arxiv.org/pdf/2305.04597">pdf</a>, <a href="https://arxiv.org/format/2305.04597">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Information Theory">cs.IT</span> </div> </div> <p class="title is-5 mathjax"> Data-Driven Bee Identification for DNA Strands </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Singhvi%2C+S">Shubhransh Singhvi</a>, <a href="/search/cs?searchtype=author&query=Boruchovsky%2C+A">Avital Boruchovsky</a>, <a href="/search/cs?searchtype=author&query=Kiah%2C+H+M">Han Mao Kiah</a>, <a href="/search/cs?searchtype=author&query=Yaakobi%2C+E">Eitan Yaakobi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2305.04597v1-abstract-short" style="display: inline;"> We study a data-driven approach to the bee identification problem for DNA strands. The bee-identification problem, introduced by Tandon et al. (2019), requires one to identify $M$ bees, each tagged by a unique barcode, via a set of $M$ noisy measurements. Later, Chrisnata et al. (2022) extended the model to case where one observes $N$ noisy measurements of each bee, and applied the model to addres… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.04597v1-abstract-full').style.display = 'inline'; document.getElementById('2305.04597v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2305.04597v1-abstract-full" style="display: none;"> We study a data-driven approach to the bee identification problem for DNA strands. The bee-identification problem, introduced by Tandon et al. (2019), requires one to identify $M$ bees, each tagged by a unique barcode, via a set of $M$ noisy measurements. Later, Chrisnata et al. (2022) extended the model to case where one observes $N$ noisy measurements of each bee, and applied the model to address the unordered nature of DNA storage systems. In such systems, a unique address is typically prepended to each DNA data block to form a DNA strand, but the address may possibly be corrupted. While clustering is usually used to identify the address of a DNA strand, this requires $\mathcal{M}^2$ data comparisons (when $\mathcal{M}$ is the number of reads). In contrast, the approach of Chrisnata et al. (2022) avoids data comparisons completely. In this work, we study an intermediate, data-driven approach to this identification task. For the binary erasure channel, we first show that we can almost surely correctly identify all DNA strands under certain mild assumptions. Then we propose a data-driven pruning procedure and demonstrate that on average the procedure uses only a fraction of $\mathcal{M}^2$ data comparisons. Specifically, for $\mathcal{M}= 2^n$ and erasure probability $p$, the expected number of data comparisons performed by the procedure is $魏\mathcal{M}^2$, where $\left(\frac{1+2p-p^2}{2}\right)^n \leq 魏\leq \left(\frac{1+p}{2}\right)^n $. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.04597v1-abstract-full').style.display = 'none'; document.getElementById('2305.04597v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Conference paper accepted at ISIT 2023</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2305.03442">arXiv:2305.03442</a> <span> [<a href="https://arxiv.org/pdf/2305.03442">pdf</a>, <a href="https://arxiv.org/format/2305.03442">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Information Theory">cs.IT</span> </div> </div> <p class="title is-5 mathjax"> Repair of Reed-Solomon Codes in the Presence of Erroneous Nodes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Kruglik%2C+S">Stanislav Kruglik</a>, <a href="/search/cs?searchtype=author&query=Luo%2C+G">Gaojun Luo</a>, <a href="/search/cs?searchtype=author&query=Kim%2C+W">Wilton Kim</a>, <a href="/search/cs?searchtype=author&query=Singhvi%2C+S">Shubhransh Singhvi</a>, <a href="/search/cs?searchtype=author&query=Kiah%2C+H+M">Han Mao Kiah</a>, <a href="/search/cs?searchtype=author&query=Ling%2C+S">San Ling</a>, <a href="/search/cs?searchtype=author&query=Wang%2C+H">Huaxiong Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2305.03442v1-abstract-short" style="display: inline;"> We consider the repair scheme of Guruswami-Wootters for the Reed-Solomon code and ask: can we correctly repair a failed node in the presence of erroneous nodes? Equivalently, we consider the collection of downloaded traces as a code and investigate its code-distance properties. We propose three lower bounds on its minimum distance and study methods to efficiently correct errors close to these boun… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.03442v1-abstract-full').style.display = 'inline'; document.getElementById('2305.03442v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2305.03442v1-abstract-full" style="display: none;"> We consider the repair scheme of Guruswami-Wootters for the Reed-Solomon code and ask: can we correctly repair a failed node in the presence of erroneous nodes? Equivalently, we consider the collection of downloaded traces as a code and investigate its code-distance properties. We propose three lower bounds on its minimum distance and study methods to efficiently correct errors close to these bounds. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.03442v1-abstract-full').style.display = 'none'; document.getElementById('2305.03442v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Accepted to IEEE International Symposium on Information Theory 2023</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2212.11489">arXiv:2212.11489</a> <span> [<a href="https://arxiv.org/pdf/2212.11489">pdf</a>, <a href="https://arxiv.org/format/2212.11489">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Information Theory">cs.IT</span> </div> </div> <p class="title is-5 mathjax"> Coding Gain for Age of Information in a Multi-source System with Erasure Channel </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Singhvi%2C+S">Shubhransh Singhvi</a>, <a href="/search/cs?searchtype=author&query=Mankar%2C+P+D">Praful D. Mankar</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2212.11489v2-abstract-short" style="display: inline;"> In our work, we study the age of information ($\AoI$) in a multi-source system where $K$ sources transmit updates of their time-varying processes via a common-aggregator node to a destination node through a channel with packet delivery errors. We analyze $\AoI$ for an $(伪, 尾, 蔚_0, 蔚_1)$-Gilbert-Elliot ($\GE$) packet erasure channel with a round-robin scheduling policy. We employ maximum distance s… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.11489v2-abstract-full').style.display = 'inline'; document.getElementById('2212.11489v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2212.11489v2-abstract-full" style="display: none;"> In our work, we study the age of information ($\AoI$) in a multi-source system where $K$ sources transmit updates of their time-varying processes via a common-aggregator node to a destination node through a channel with packet delivery errors. We analyze $\AoI$ for an $(伪, 尾, 蔚_0, 蔚_1)$-Gilbert-Elliot ($\GE$) packet erasure channel with a round-robin scheduling policy. We employ maximum distance separable ($\MDS$) scheme at aggregator for encoding the multi-source updates. We characterize the mean $\AoI$ for the $\MDS$ coded system for the case of large blocklengths. We further show that the \emph{optimal coding rate} that achieves maximum \emph{coding gain} over the uncoded system is $n(1-\pers)-\smallO(n)$, where $\pers \triangleq \frac尾{伪+尾}蔚_0 + \frac伪{伪+尾}蔚_1$, and this maximum coding gain is $(1+\pers)/(1+\smallO(1))$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.11489v2-abstract-full').style.display = 'none'; document.getElementById('2212.11489v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 April, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Accepted at IEEE-ITW 2023</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2207.04025">arXiv:2207.04025</a> <span> [<a href="https://arxiv.org/pdf/2207.04025">pdf</a>, <a href="https://arxiv.org/ps/2207.04025">ps</a>, <a href="https://arxiv.org/format/2207.04025">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Information Theory">cs.IT</span> </div> </div> <p class="title is-5 mathjax"> Rate-Optimal Streaming Codes Over the Three-Node Decode-And-Forward Relay Network </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Singhvi%2C+S">Shubhransh Singhvi</a>, <a href="/search/cs?searchtype=author&query=R.%2C+G">Gayathri R.</a>, <a href="/search/cs?searchtype=author&query=Kumar%2C+P+V">P. Vijay Kumar</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2207.04025v2-abstract-short" style="display: inline;"> In this paper, we study the three-node Decode-and-Forward (D&F) relay network subject to random and burst packet erasures. The source wishes to transmit an infinite stream of packets to the destination via the relay. The three-node D&F relay network is constrained by a decoding delay of T packets, i.e., the packet transmitted by the source at time i must be decoded by the destination by time i+T.… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.04025v2-abstract-full').style.display = 'inline'; document.getElementById('2207.04025v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2207.04025v2-abstract-full" style="display: none;"> In this paper, we study the three-node Decode-and-Forward (D&F) relay network subject to random and burst packet erasures. The source wishes to transmit an infinite stream of packets to the destination via the relay. The three-node D&F relay network is constrained by a decoding delay of T packets, i.e., the packet transmitted by the source at time i must be decoded by the destination by time i+T. For the individual channels from source to relay and relay to destination, we assume a delay-constrained sliding-window (DCSW) based packet-erasure model that can be viewed as a tractable approximation to the commonly-accepted Gilbert-Elliot channel model. Under the model, any time-window of width w contains either up to a random erasure or else erasure burst of length at most b (>= a). Thus the source-relay and relay-destination channels are modeled as (a_1, b_1, w_1, T_1) and (a_2, b_2, w_2, T_2) DCSW channels. We first derive an upper bound on the capacity of the three-node D&F relay network. We then show that the upper bound is tight for the parameter regime: max{b_1, b_2}|(T-b_1-b_2-max{a_1, a_2}+1), a1=a2 OR b1=b2 by constructing streaming codes achieving the bound. The code construction requires field size linear in T, and has decoding complexity equivalent to that of decoding an MDS code. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.04025v2-abstract-full').style.display = 'none'; document.getElementById('2207.04025v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 November, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Published at ISIT 2022</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2202.03024">arXiv:2202.03024</a> <span> [<a href="https://arxiv.org/pdf/2202.03024">pdf</a>, <a href="https://arxiv.org/format/2202.03024">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Information Theory">cs.IT</span> </div> </div> <p class="title is-5 mathjax"> The Input and Output Entropies of the $k$-Deletion/Insertion Channel </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Singhvi%2C+S">Shubhransh Singhvi</a>, <a href="/search/cs?searchtype=author&query=Sabary%2C+O">Omer Sabary</a>, <a href="/search/cs?searchtype=author&query=Bar-Lev%2C+D">Daniella Bar-Lev</a>, <a href="/search/cs?searchtype=author&query=Yaakobi%2C+E">Eitan Yaakobi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2202.03024v2-abstract-short" style="display: inline;"> The channel output entropy of a transmitted word is the entropy of the possible channel outputs and similarly, the input entropy of a received word is the entropy of all possible transmitted words. The goal of this work is to study these entropy values for the k-deletion, k-insertion channel, where exactly k symbols are deleted, and inserted in the transmitted word, respectively. If all possible w… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2202.03024v2-abstract-full').style.display = 'inline'; document.getElementById('2202.03024v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2202.03024v2-abstract-full" style="display: none;"> The channel output entropy of a transmitted word is the entropy of the possible channel outputs and similarly, the input entropy of a received word is the entropy of all possible transmitted words. The goal of this work is to study these entropy values for the k-deletion, k-insertion channel, where exactly k symbols are deleted, and inserted in the transmitted word, respectively. If all possible words are transmitted with the same probability then studying the input and output entropies is equivalent. For both the 1-insertion and 1-deletion channels, it is proved that among all words with a fixed number of runs, the input entropy is minimized for words with a skewed distribution of their run lengths and it is maximized for words with a balanced distribution of their run lengths. Among our results, we establish a conjecture by Atashpendar et al. which claims that for the binary 1-deletion, the input entropy is maximized for the alternating words. This conjecture is also verified for the 2-deletion channel, where it is proved that constant words with a single run minimize the input entropy. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2202.03024v2-abstract-full').style.display = 'none'; document.getElementById('2202.03024v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 June, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 February, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2022. </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" 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