Towards an algebraic network information theory: Simultaneous joint typicality decoding

Lim, Sung Hoon; Feng, Chen; Pastore, Adriano; Nazer, Bobak; Gastpar, Michael

doi:10.1109/isit.2017.8006843

Cited by 10 publications

(15 citation statements)

References 30 publications

(28 reference statements)

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“…However, this implies immediately that decoder 2 cannot decode both codewords reliably. Indeed, if decoder 2 could decode both codewords, the achievable sum rate in (6) directly contradicts the upper bound in (5). Notice that this argument holds for any value of N 2 , we conclude that the same sequence of codes cannot be used as multiple-access codes for the GMAC(SNR 2 ), regardless of the value of SNR 2 .…”

Section: Dualitymentioning

confidence: 77%

“…More recently, nested linear codes are shown to be good computation codes for a general discrete-memoryless MAC [5]. Focusing on the Gaussian MAC, we have the following result [4].…”

Section: Problem Statement and Definitionsmentioning

confidence: 80%

“…On the other hand, some recent work (e.g. [5]) suggests that such algebraic structure could be obstacles for the purpose of multiple-access. This note makes a simple yet interesting observation on the duality between the codes used for communication and the codes used for computation on the two-user Gaussian multiple-access channel (MAC).…”

Section: Introductionmentioning

confidence: 99%

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On the duality between multiple-access codes and computation codes

Zhu

Lim

Gastpar

2017

2017 Information Theory and Applications Workshop (ITA)

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Abstract-For a two-user Gaussian multiple access channel, computation codes are designed for the scenarios where the decoder is not interested in decoding the two codewords, but only the sum of them. It has been observed that good computation codes should possess some algebraic structure. In this note, we expose the fact that such algebraic structure could undermine the capability of the codes for recovering the messages, i.e., for the purpose of multiple-access. Particularly, we establish duality results between the codes which are good for computation and the codes which are good for multiple access.

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Section: Dualitymentioning

confidence: 77%

“…More recently, nested linear codes are shown to be good computation codes for a general discrete-memoryless MAC [5]. Focusing on the Gaussian MAC, we have the following result [4].…”

Section: Problem Statement and Definitionsmentioning

confidence: 80%

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On the duality between multiple-access codes and computation codes

Zhu

Lim

Gastpar

2017

2017 Information Theory and Applications Workshop (ITA)

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“…, x k ), X 1 = X 2 = · · · = X k = F q , by random homologous code ensembles was studied in [20]. For the sake of completeness, we review the main result in [20] on which we build the achievability of the capacity region for the k-sender DM-MAC. Let A denote the set of rank deficient k × k matrices over F q .…”

Section: A Shapingmentioning

confidence: 99%

“…improved their analysis to establish a larger achievable rate region for message communication [20], which is still strictly smaller than the capacity region. Apparently, structured coding, even based on the promising new technique of nested coset codes, can only play a complementary role to random coding.…”

mentioning

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 Magic of Superposition: A Survey on Simultaneous Transmission Based Wireless Systems

2022

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In conventional communication systems, any interference between two communicating points is regarded as unwanted noise since it distorts the received signals. On the other hand, allowing simultaneous transmission and intentionally accepting the superposition of signals and even benefiting from it have been considered for a range of wireless applications. As prominent examples, NOMA, joint sourcechannel coding, and the computation codes are designed to exploit this scenario. They also inspired many other fundamental works from network coding to consensus algorithms. Especially, federated learning is an emerging technology that can be applied to distributed machine learning networks by allowing simultaneous transmission. Although various simultaneous transmission applications exist independently in the literature, their main contributions are all based on the same principle; the superposition property. In this survey, we aim to emphasize the connections between these studies and provide a guide for the readers on the wireless communication techniques that benefit from the superposition of signals. We classify the existing literature depending on their purpose and application area and present their contributions. The survey shows that simultaneous transmission can bring scalability, security, low-latency, low-complexity and energy efficiency for certain distributed wireless scenarios which are inevitable with the emerging wireless technologies.

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Towards an algebraic network information theory: Simultaneous joint typicality decoding

Cited by 10 publications

References 30 publications

On the duality between multiple-access codes and computation codes

On the duality between multiple-access codes and computation codes

Homologous codes for multiple access channels

The Magic of Superposition: A Survey on Simultaneous Transmission Based Wireless Systems

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