Beyond group capacity in multi-terminal communications

Heidari, Mohsen; Shirani, Farhad; Pradhan, S. Sandeep

doi:10.1109/isit.2015.7282822

Cited by 4 publications

(8 citation statements)

References 21 publications

(33 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, structured codes were used to design coding strategies for joint source-channel coding problems, [11], [12], [13], [14], [15]. A graph-theoretic framework was introduced in [11], [12] to improve the joint source-channel coding schemes both in the MAC and the broadcast channel.…”

Section: Introductionmentioning

confidence: 99%

New sufficient conditions for Multiple-Access Channel with correlated sources

Heidari

Shirani

Pradhan

2016

2016 IEEE International Symposium on Information Theory (ISIT)

Self Cite

View full text Add to dashboard Cite

The problem of three-user Multiple-Access Channel (MAC) with correlated sources is investigated. An extension to the CoverEl Gamal-Salehi (CES) scheme is introduced. We use a combination of this scheme with linear codes and propose a new coding strategy. We derive new sufficient conditions to transmit correlated sources reliably. We consider an example of three-user MAC with binary inputs. Using this example, we show strict improvements over the CES scheme.

show abstract

Section: Introductionmentioning

confidence: 99%

New sufficient conditions for Multiple-Access Channel with correlated sources

Heidari

Shirani

Pradhan

2016

2016 IEEE International Symposium on Information Theory (ISIT)

Self Cite

View full text Add to dashboard Cite

show abstract

“…In our earlier work, we considered a special class of QGCs which is called transversal group codes [9].…”

Section: Proofmentioning

confidence: 99%

“…Performance limits of transversal codes for point-to-point as well as certain multi-terminal problems are investigated in [11].…”

Section: B Definitionsmentioning

confidence: 99%

“…It is shown in [9] that the largest achievable region using group codes is R i ≤ min{I(Z; Y ), 2I(Z; Y |[Z] 1 )}, where Z = X 1 + X 2 and X 1 and X 2 are uniform over Z 4 . It is shown in [11] that transversal group codes achieve…”

Section: Computation Over Macmentioning

confidence: 99%

“…Since group codes are closed under the group addition, these subgroups put a penalty on the transmission rates. Based on this observation, in our earlier attempt, we introduced a class of structured codes called transversal group codes [11]. These codes are built over cyclic groups.…”

mentioning

confidence: 99%

See 2 more Smart Citations

How to compute modulo prime-power sums

Heidari¹,

Shirani²,

Pradhan³

2016

2016 IEEE International Symposium on Information Theory (ISIT)

Self Cite

View full text Add to dashboard Cite

A new class of structured codes called Quasi Group Codes (QGC) is introduced. A QGC is a subset of a group code. In contrast with group codes, QGCs are not closed under group addition. The parameters of the QGC can be chosen such that the size of C + C is equal to any number between |C| and |C| 2 . We analyze the performance of a specific class of QGCs. This class of QGCs is constructed by assigning single-letter distributions to the indices of the codewords in a group code. Then, the QGC is defined as the set of codewords whose index is in the typical set corresponding to these single-letter distributions.The asymptotic performance limits of this class of QGCs is characterized using single-letter information quantities. Corresponding covering and packing bounds are derived. It is shown that the point-to-point channel capacity and optimal rate-distortion function are achievable using QGCs. Coding strategies based on QGCs are introduced for three fundamental multi-terminal problems: the Körner-Marton problem for modulo prime-power sums, computation over the multiple access channel (MAC), and MAC with distributed states. For each problem a single-letter achievable rate-region is derived. It is shown, through examples, that the coding strategies improve upon the previous strategies based on unstructured codes, linear codes and group codes. code ensemble, and characterize the asymptotic performance using single-letter information quantities. By choosing the single-letter distribution on the indices one can operate anywhere in the spectrum between the two extremes: group codes and unstructured codes.The contributions of this work are as follows. A new class of codes over groups called Quasi Group Codes (QGC) is introduced. These codes are constructed by taking subsets of group codes. This work considers QGCs over cyclic groups Z p r . One can use the fundamental theorem of finitely generated Abelian groups to generalize the results of this paper to QGCs over non-cyclic finite Abelian groups.Information-theoretic characterizations for the asymptotic performance limits and properties of QGCs for source coding and channel coding problems are derived in terms of single-letter information quantities.Covering and packing bounds are derived for an ensemble of QGCs. Next, a binning technique for the QGCs is developed by constructing nested QGCs. As a result of these bounds, the PtP channel capacity and optimal rate-distortion function of sources are shown to be achievable using nested QGCs. The applications of QGCs in some multi-terminal communications problems are considered. More specifically our study includes the following problems:Distributed Source Coding: A more general version of Körner-Marton problem is considered. In this problem, there are two distributed sources taking values from Z p r . The sources are to be compressed in a distributed fashion. The decoder wishes to compute the modulo p r -addition of the sources losslessly.Computation over MAC: In this problem, two transmitters wish to communicate independent i...

show abstract