Empirical Properties of Good Channel Codes

Ding, Qinghua and Jaggi, Sidharth and Vatedka, Shashank and et al, . (2020) Empirical Properties of Good Channel Codes. In: 2020 IEEE International Symposium on Information Theory, ISIT 2020, 21 July 2020through 26 July 2020, Los Angeles.

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Abstract

In this article, we revisit the classical problem of channel coding and obtain novel results on properties of capacity- achieving codes. Specifically, we give a linear algebraic characterization of the set of capacity-achieving input distributions for discrete memoryless channels. This allows us to characterize the dimension of the manifold on which the capacity-achieving distributions lie. We then proceed by examining empirical properties of capacity-achieving codebooks by showing that the joint-type of k-tuples of codewords in a good code must be close to the k- fold product of the capacity-achieving input distribution. While this conforms with the intuition that all capacity-achieving codes must behave like random capacity-achieving codes, we also show that some properties of random coding ensembles do not hold for all codes. We prove this by showing that there exist pairs of communication problems such that random code ensembles simultaneously attain capacities of both problems, but certain (superposition ensembles) do not.Due to lack of space, several proofs have been omitted but can be found at https://sites.google.com/view/yihan/ [1] © 2020 IEEE.

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IITH Creators:
IITH CreatorsORCiD
Vatedka, Shashankhttps://orcid.org/0000-0003-2384-9392
Item Type: Conference or Workshop Item (Paper)
Additional Information: 1Given any memoryless channel W , we will interchangeably use “W -good” The work of Sidharth Jaggi and Yihan Zhang was supported by the Research or “capacity-achieving” to describe codes which have rate arbitrarily close to Grants Council (RGC) of Hong Kong under Project Numbers 14300617, the capacity of W and have average error probability decaying in blocklength
Uncontrolled Keywords: Capacity achieving distribution; Classical problems; Communication problems; Discrete memoryless channels; Empirical properties; Input distributions; Linear-algebraic; Random capacity
Subjects: Electrical Engineering
Divisions: Department of Electrical Engineering
Depositing User: . LibTrainee 2021
Date Deposited: 02 Nov 2022 09:40
Last Modified: 02 Nov 2022 09:40
URI: http://raiith.iith.ac.in/id/eprint/11132
Publisher URL: http://doi.org/10.1109/ISIT44484.2020.9174129
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