--- _id: '6678' abstract: - lang: eng text: We survey coding techniques that enable reliable transmission at rates that approach the capacity of an arbitrary discrete memoryless channel. In particular, we take the point of view of modern coding theory and discuss how recent advances in coding for symmetric channels help provide more efficient solutions for the asymmetric case. We consider, in more detail, three basic coding paradigms. The first one is Gallager's scheme that consists of concatenating a linear code with a non-linear mapping so that the input distribution can be appropriately shaped. We explicitly show that both polar codes and spatially coupled codes can be employed in this scenario. Furthermore, we derive a scaling law between the gap to capacity, the cardinality of the input and output alphabets, and the required size of the mapper. The second one is an integrated scheme in which the code is used both for source coding, in order to create codewords distributed according to the capacity-achieving input distribution, and for channel coding, in order to provide error protection. Such a technique has been recently introduced by Honda and Yamamoto in the context of polar codes, and we show how to apply it also to the design of sparse graph codes. The third paradigm is based on an idea of Böcherer and Mathar, and separates the two tasks of source coding and channel coding by a chaining construction that binds together several codewords. We present conditions for the source code and the channel code, and we describe how to combine any source code with any channel code that fulfill those conditions, in order to provide capacity-achieving schemes for asymmetric channels. In particular, we show that polar codes, spatially coupled codes, and homophonic codes are suitable as basic building blocks of the proposed coding strategy. Rather than focusing on the exact details of the schemes, the purpose of this tutorial is to present different coding techniques that can then be implemented with many variants. There is no absolute winner and, in order to understand the most suitable technique for a specific application scenario, we provide a detailed comparison that takes into account several performance metrics. article_type: original author: - first_name: Marco full_name: Mondelli, Marco id: 27EB676C-8706-11E9-9510-7717E6697425 last_name: Mondelli orcid: 0000-0002-3242-7020 - first_name: Hamed full_name: Hassani, Hamed last_name: Hassani - first_name: 'Rudiger ' full_name: 'Urbanke, Rudiger ' last_name: Urbanke citation: ama: Mondelli M, Hassani H, Urbanke R. How to achieve the capacity of asymmetric channels. IEEE Transactions on Information Theory. 2018;64(5):3371-3393. doi:10.1109/tit.2018.2789885 apa: Mondelli, M., Hassani, H., & Urbanke, R. (2018). How to achieve the capacity of asymmetric channels. IEEE Transactions on Information Theory. IEEE. https://doi.org/10.1109/tit.2018.2789885 chicago: Mondelli, Marco, Hamed Hassani, and Rudiger Urbanke. “How to Achieve the Capacity of Asymmetric Channels.” IEEE Transactions on Information Theory. IEEE, 2018. https://doi.org/10.1109/tit.2018.2789885. ieee: M. Mondelli, H. Hassani, and R. Urbanke, “How to achieve the capacity of asymmetric channels,” IEEE Transactions on Information Theory, vol. 64, no. 5. IEEE, pp. 3371–3393, 2018. ista: Mondelli M, Hassani H, Urbanke R. 2018. How to achieve the capacity of asymmetric channels. IEEE Transactions on Information Theory. 64(5), 3371–3393. mla: Mondelli, Marco, et al. “How to Achieve the Capacity of Asymmetric Channels.” IEEE Transactions on Information Theory, vol. 64, no. 5, IEEE, 2018, pp. 3371–93, doi:10.1109/tit.2018.2789885. short: M. Mondelli, H. Hassani, R. Urbanke, IEEE Transactions on Information Theory 64 (2018) 3371–3393. date_created: 2019-07-24T12:38:49Z date_published: 2018-05-01T00:00:00Z date_updated: 2023-02-23T12:50:46Z day: '01' doi: 10.1109/tit.2018.2789885 extern: '1' external_id: arxiv: - '1406.7373' intvolume: ' 64' issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1406.7373 month: '05' oa: 1 oa_version: Preprint page: 3371-3393 publication: IEEE Transactions on Information Theory publication_identifier: issn: - 0018-9448 - 1557-9654 publication_status: published publisher: IEEE quality_controlled: '1' related_material: record: - id: '6740' relation: earlier_version status: public status: public title: How to achieve the capacity of asymmetric channels type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 64 year: '2018' ...