Bounds on algebraic code capacities for noisy channels. II

Ahlswede, Rudolf; Gemma, J.

doi:10.1016/s0019-9958(71)90783-2

Cited by 12 publications

(5 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [6], the capacity of group codes for certain classes of channels has been computed. Further results on the capacity of group codes were established in [7], [8]. The capacity of group codes over a class of channels exhibiting symmetries with respect to the action of a finite Abelian group has been investigated in [11].…”

Section: Introductionmentioning

confidence: 99%

Abelian Group Codes for Channel Coding and Source Coding

Sahebi

Pradhan

2015

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

In this paper, we study the asymptotic performance of Abelian group codes for the the channel coding problem for arbitrary discrete (finite alphabet) memoryless channels as well as the lossy source coding problem for arbitrary discrete (finite alphabet) memoryless sources. For the channel coding problem, we find the capacity characterized in a single-letter information-theoretic form. This simplifies to the symmetric capacity of the channel when the underlying group is a field. For the source coding problem, we derive the achievable rate-distortion function that is characterized in a single-letter information-theoretic form. When the underlying group is a field, it simplifies to the symmetric rate-distortion function. We give several illustrative examples. Due to the non-symmetric nature of the sources and channels considered, our analysis uses a synergy of information-theoretic and group-theoretic tools.

show abstract

Section: Introductionmentioning

confidence: 99%

Abelian Group Codes for Channel Coding and Source Coding

Sahebi

Pradhan

2015

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

show abstract

“…In [5], the capacity of group codes for certain classes of channels has been computed. Further results on the capacity of group codes were established in [6], [7]. The capacity of group codes over a class of channels exhibiting symmetries with respect to the action of a finite Abelian group has been investigated in [9].…”

Section: Introductionmentioning

confidence: 99%

Abelian Group Codes for Source Coding and Channel Coding

Sahebi,

Pradhan

2013

Preprint

View full text Add to dashboard Cite

In this paper, we study the asymptotic performance of Abelian group codes for the lossy source coding problem for arbitrary discrete (finite alphabet) memoryless sources as well as the channel coding problem for arbitrary discrete (finite alphabet) memoryless channels. For the source coding problem, we derive an achievable rate-distortion function that is characterized in a single-letter information-theoretic form using the ensemble of Abelian group codes. When the underlying group is a field, it simplifies to the symmetric rate-distortion function. Similarly, for the channel coding problem, we find an achievable rate characterized in a single-letter information-theoretic form using group codes. This simplifies to the symmetric capacity of the channel when the underlying group is a field. We compute the rate-distortion function and the achievable rate for several examples of sources and channels. Due to the non-symmetric nature of the sources and channels considered, our analysis uses a synergy of information theoretic and group-theoretic tools.

show abstract

“…In [1], the capacity of group codes for certain classes of channels has been computed. Further results on the capacity of group codes were established in [2], [3]. The capacity of group codes over a class of channels exhibiting symmetries with respect to the action of a finite Abelian group has been investigated in [5].…”

Section: Introductionmentioning

confidence: 99%

On the capacity of Abelian group codes over discrete memoryless channels

Sahebi

Pradhan

2011

2011 IEEE International Symposium on Information Theory Proceedings

View full text Add to dashboard Cite

Abstract-For most discrete memoryless channels, there does not exist a linear code which uses all of the channel's input symbols. Therefore, linearity of the code for such channels is a very restrictive condition and there should be a loosening of the algebraic structure of the code to a degree that the code can admit any channel input alphabet. For any channel input alphabet size, there always exists an Abelian group structure defined on the alphabet. We investigate the capacity of Abelian group codes over discrete memoryless channels and provide lower and upper bounds on the capacity.

show abstract

Bounds on algebraic code capacities for noisy channels. II

Cited by 12 publications

References 7 publications

Abelian Group Codes for Channel Coding and Source Coding

Abelian Group Codes for Channel Coding and Source Coding

Abelian Group Codes for Source Coding and Channel Coding

On the capacity of Abelian group codes over discrete memoryless channels

Contact Info

Product

Resources

About