Optimal index coding with min-max probability of error over fading channels

Thomas, Anoop; Kavitha, R.; Chandramouli, A. B.; Rajan, B. Sundar

doi:10.1109/pimrc.2015.7343423

Cited by 19 publications

(14 citation statements)

References 9 publications

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“…Further, if we are interested only in giving the best possible performance to a chosen customer who has large amount of side information and not in giving the best possible performance to every receiver, then using a 2 n -PSK/QAM would be a better strategy. The mapping and 2-D transmission scheme introduced in this paper are also applicable to index coding over fading channels which was considered in [7].…”

Section: Discussionmentioning

confidence: 99%

Noisy Index Coding with PSK and QAM

Mahesh,

Rajan

2016

Preprint

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Noisy index coding problems over AWGN channel are considered. For a given index coding problem and a chosen scalar linear index code of length N , we propose to transmit the N index coded bits as a single signal from a 2 N -PSK constellation. By transmitting the index coded bits in this way, there is an N/2 -fold reduction in the bandwidth consumed. Also, receivers with side information satisfying certain conditions get coding gain relative to a receiver with no side information. This coding gain is due to proper utilization of their side information and hence is called "PSK side information coding gain (PSK-SICG)". A necessary and sufficient condition for a receiver to get PSK-SICG is presented. An algorithm to map the index coded bits to PSK signal set such that the PSK-SICG obtained is maximized for the receiver with maximum side information is given. We go on to show that instead of transmitting the N index coded bits as a signal from 2 N -PSK, we can as well transmit them as a signal from 2 N -QAM and all the results including the necessary and sufficient condition to get coding gain holds. We prove that sending the index coded bits as a QAM signal is better than sending them as a PSK signal when the receivers see an effective signal set of eight points or more.

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Section: Discussionmentioning

confidence: 99%

Noisy Index Coding with PSK and QAM

Mahesh,

Rajan

2016

Preprint

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“…. n where each A i is a c × n matrix in which all elements in the i-th column are ones and the rest all are zeros as given in (8).…”

Section: Equivalent Network Coding Problemmentioning

confidence: 99%

“…In fact, different receivers may use different number of transmissions of the source. It has been shown in [8] that there can be several linear optimal index codes in terms of lowest number of transmissions for an IC problem, but among them one needs to identify the linear optimal index code which minimizes the maximum number of transmissions that is required by any receiver in decoding its desired message. The motivation for this comes from the fact that each of the transmitted symbols is error prone in a wireless scenario and lesser the number of transmissions used in decoding the desired message, lesser will be its probability of error.…”

Section: Introductionmentioning

confidence: 99%

“…Hence among all the codes with the same length, the one for which the maximum number of transmissions used by any receiver is the minimum, will have minimummaximum error probability. This has already been discussed in [8] for single uniprior IC problems where a method to find a best linear solution in terms of minimum-maximum error probability among all codes with the optimal length is given.…”

Section: Introductionmentioning

confidence: 99%

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On the number of optimal linear index codes for unicast index coding problems

Kavitha¹,

Ambadi²,

Rajan³

2016

2016 IEEE Wireless Communications and Networking Conference

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Abstract-An index coding problem arises when there is a single source with a number of messages and multiple receivers each wanting a subset of messages and knowing a different set of messages a priori. The noiseless Index Coding Problem is to identify the minimum number of transmissions (optimal length) to be made by the source through noiseless channels so that all receivers can decode their wanted messages using the transmitted symbols and their respective prior information. Recently [8], it is shown that different optimal length codes perform differently in a noisy channel. Towards identifying the best optimal length index code one needs to know the number of optimal length index codes. In this paper we present results on the number of optimal length index codes making use of the representation of an index coding problem by an equivalent network code. Our formulation results in matrices of smaller sizes compared to the approach of Kotter and Medard [6]. Our formulation leads to a lower bound on the minimum number of optimal length codes possible for all unicast index coding problems [1] which is met with equality for several special cases of the unicast index coding problem. A method to identify the optimal length codes which lead to minimum-maximum probability of error is also presented.

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“…. , x k+(m−1)K } (the set of message symbols appearing in x k + x k+K + x k+2K + • • • + x k+(m−1)K ), every message symbol x k+jK , 0 ≤ j ≤ m−1, is in the antidote of every receiver R k+iK , 0 ≤ i = j ≤ m− 1, according to given antidote pattern in (6). In other words,…”

Section: Lifting Constructionmentioning

confidence: 99%

A Lifting Construction for Scalar Linear Index Codes

Bhattaram,

Vaddi,

Rajan

2015

Preprint

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This paper deals with scalar linear index codes for canonical multiple unicast index coding problems where there is a source with K messages and there are K receivers each wanting a unique message and having symmetric (with respect to the receiver index) antidotes (side information). Optimal scalar linear index codes for several such instances of this class of problems have been reported in [9]. These codes can be viewed as special cases of the symmetric unicast index coding problems discussed in [1]. In this paper a lifting construction is given which constructs a sequence of multiple unicast index problems starting from a given multiple unicast index coding problem. Also, it is shown that if an optimal scalar linear index code is known for the problem given starting problem then optimal scalar linear index codes can be obtained from the known code for all the problems arising from the proposed lifting construction. For several of the known classes of multiple unicast problems our construction is used to obtain several sequences of multiple unicast problem with optimal scalar linear index codes. 1

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Optimal index coding with min-max probability of error over fading channels

Cited by 19 publications

References 9 publications

Noisy Index Coding with PSK and QAM

Noisy Index Coding with PSK and QAM

On the number of optimal linear index codes for unicast index coding problems

A Lifting Construction for Scalar Linear Index Codes

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