A new achievable rate region for the 3-user discrete memoryless interference channel

Padakandla, Arun; Sahebi, Aria G.; Pradhan, S. Sandeep

doi:10.1109/isit.2012.6283913

Cited by 21 publications

(39 citation statements)

References 15 publications

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“…In our prior work, we developed an inner bound to the optimal rate-distortion region for the distributed source coding problem [23] in which cyclic group codes were used as building blocks in the coding schemes. Similar coding approaches were applied for the interference channel and the broadcast channel in [26], [27]. The motivation for studying Abelian group codes beyond the non-existence of finite fields over arbitrary alphabets is the following.…”

Section: Introductionmentioning

confidence: 99%

Abelian Group Codes for Channel Coding and Source Coding

Sahebi

Pradhan

2015

IEEE Trans. Inform. Theory

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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.

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Section: Introductionmentioning

confidence: 99%

Abelian Group Codes for Channel Coding and Source Coding

Sahebi

Pradhan

2015

IEEE Trans. Inform. Theory

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“…where R (j) L (U 1 , U 2 , X 1 , X 2 ), j = 2, 3, is the set of rate pairs (R 1 , R 2 ) satisfying (11) or (12) for the DM-MAC p(y j |x 1 , x 2 ) with specified p(u 1 , x 1 ) and p(u 2 , x 2 ). The achievable rate region consisting of all rate pairs satisfying (21)-(23) after convexification via time sharing is sketched in Fig.…”

Section: Discussionmentioning

confidence: 99%

“…where R (j) L (U 1 , U 2 , X 1 , X 2 ), j = 1, 2, is the set of rate pairs (R 1 , R 2 ) satisfying (11) or (12) for the DM-MAC p(y j |x 1 , x 2 ). The argument in the proof of Theorem 1 can be applied to both of the DM-MACs p(y 1 |x 1 , x 2 ) and p(y 2 |x 1 , x 2 ).…”

Section: Multiple-receiver Multiple Access Channelsmentioning

confidence: 99%

Homologous codes for multiple access channels

Sen

Kim

2017

2017 IEEE International Symposium on Information Theory (ISIT)

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Building on recent development by Padakandla and Pradhan, and by Lim, Feng, Pastore, Nazer, and Gastpar, this paper studies the potential of structured nested coset coding as a complete replacement for random coding in network information theory. The roles of two techniques used in nested coset coding to generate nonuniform codewords, namely, shaping and channel transformation, are clarified and illustrated via the simple example of the two-sender multiple access channel. While individually deficient, the optimal combination of shaping and channel transformation is shown to achieve the same performance as traditional random codes for the general two-sender multiple access channel. The achievability proof of the capacity region is extended to the multiple access channels with more than two senders, and with one or more receivers. A quantization argument consistent with the construction of nested coset codes is presented to prove achievability for their Gaussian counterparts. These results open up new possibilities of utilizing nested coset codes with the same generator matrix for a broader class of applications. I. INTRODUCTIONRandom independently and identically distributed (i.i.d.) code ensembles play a fundamental role in network information theory, with most existing coding schemes built on them; see, for example, [1]- [3]. As shown by the classical example by Körner and Marton [4], however, using the same code at multiple users can achieve strictly better performance for some communication problems. Recent studies illustrate the benefit of such structured coding for computing linear combinations in [5]-[10], for the interference channels in [11]-[14], and for the multiple access channels with state information in [15]. Consequently, there has been a flurry of research activities on structured coding in network information theory, facilitated in part by several standalone workshops and tutorials at major conferences by leading researchers.Most of the existing results are based on lattice codes or linear codes on finite alphabets. Recently, Padakandla and Pradhan [15] brought a new dimension to the arsenal of structured coding by developing nested coset codes for network information theory; see also Miyake [16] for nested coset codes for point-to-point communication. In these nested coset coding schemes, a coset code of a rate higher than the target is first generated randomly. A codeword of a desired property (such as type or joint type) is then selected from a subset (a coset of a subcode). This construction is reminiscent of the multicoding scheme in Gelfand-Pinsker coding for channels with state and Marton coding for broadcast channels. But in a sense, nested coset coding is more fundamental in that the scheme at its core is relevant even for single-user communication. By a careful combination of individual and common parts of coset codes, the proposed coding scheme in [15] achieves rates for multiple access channels (MACs) with state beyond what can be achieved by existing random or structured coding sche...

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“…The algebraic structure is exploited toward achieving better source compression. This approach has been applied in a variety of communication settings such as lossy distributed source coding [9], multiple access channels (MAC) with states [17], interference channels [18], [20], computation over multiple-access channels [8], [10], and broadcast channels [19]. Most of these works have used schemes based on linear code ensembles.…”

Section: Introductionmentioning

confidence: 99%

Beyond group capacity in multi-terminal communications

Heidari

Shirani

Pradhan

2015

2015 IEEE International Symposium on Information Theory (ISIT)

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A new structured coding scheme based on transver sal group codes is proposed. We investigate the information theoretic performance limits for this strategy in multi-terminal communications. Achievability results are derived for lossless reconstruction of sum of two sources. In addition, a new rate region is presented for the problem of computation over multiple access channel . We show that the application of the new coding strategy, results in strict gains in terms of achievable rates in both settings.

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A new achievable rate region for the 3-user discrete memoryless interference channel

Cited by 21 publications

References 15 publications

Abelian Group Codes for Channel Coding and Source Coding

Abelian Group Codes for Channel Coding and Source Coding

Homologous codes for multiple access channels

Beyond group capacity in multi-terminal communications

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