---
_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
arxiv: 1
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. <i>IEEE Transactions on Information Theory</i>. 2018;64(5):3371-3393.
    doi:<a href="https://doi.org/10.1109/tit.2018.2789885">10.1109/tit.2018.2789885</a>
  apa: Mondelli, M., Hassani, H., &#38; Urbanke, R. (2018). How to achieve the capacity
    of asymmetric channels. <i>IEEE Transactions on Information Theory</i>. IEEE.
    <a href="https://doi.org/10.1109/tit.2018.2789885">https://doi.org/10.1109/tit.2018.2789885</a>
  chicago: Mondelli, Marco, Hamed Hassani, and Rudiger  Urbanke. “How to Achieve the
    Capacity of Asymmetric Channels.” <i>IEEE Transactions on Information Theory</i>.
    IEEE, 2018. <a href="https://doi.org/10.1109/tit.2018.2789885">https://doi.org/10.1109/tit.2018.2789885</a>.
  ieee: M. Mondelli, H. Hassani, and R. Urbanke, “How to achieve the capacity of asymmetric
    channels,” <i>IEEE Transactions on Information Theory</i>, 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.”
    <i>IEEE Transactions on Information Theory</i>, vol. 64, no. 5, IEEE, 2018, pp.
    3371–93, doi:<a href="https://doi.org/10.1109/tit.2018.2789885">10.1109/tit.2018.2789885</a>.
  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'
...