Degrees of freedom of interference channel with rank-deficient transfer matrix

Ramakrishnan, Abinesh; Krishnamurthy, Sundar R.; Jafar, Syed A.; Yu, Yaming

doi:10.1109/isit.2014.6875027

Degrees of freedom of interference channel with rank-deficient transfer matrix

Ramakrishnan

¹

,

Krishnamurthy

²

,

Jafar

³

et al. 2014

2014 IEEE International Symposium on Information Theory

3

0

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Abstract-We consider the interference channel with K transmitters and K receivers all having a single antenna, wherein the K × K transfer matrix representing this channel has rank D (D < K) . The degrees of freedom (DoF) of such channels are not known as the rank deficiency in the transfer matrix creates algebraic dependencies between the channel coefficients. We present a modified version of the [CJ08] alignment scheme, to handle these dependencies while aligning interference, and state the sufficient conditions for achieving half rate per user using this scheme. The difficulties in proving these sufficient conditions are shown for K = 4 and K = 5. We also show that these sufficient conditions are not satisfied for K ≥ 6.

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Canonical conditions for K/2 degrees of freedom

Stotz

¹

,

Jafar

²

,

Bölcskei

³

et al. 2016

2016 IEEE International Symposium on Information Theory (ISIT)

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We present a condition for 1/2 degree of freedom for each user in constant K-user single-antenna interference channels. This condition is sufficient for all and necessary for almost all channel matrices. Moreover, it applies to all channel topologies, i.e., to fully-connected channels as well as channels that have individual links absent, reflected by corresponding zeros in the channel matrix. Moreover, it captures the essence of interference alignment by virtue of being expressed in terms of a generic injectivity condition that guarantees separability of signal and interference. Finally, we provide codebook constructions achieving 1/2 degree of freedom for each user for all channel matrices satisfying the condition we identified.

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Canonical Conditions for K/2 Degrees of Freedom

Gul¹,

Stotz

²

,

Jafar

³

et al. 2022

IEEE Trans. Inform. Theory

2

0

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We present a condition for 1/2 degree of freedom for each user in constant K-user single-antenna interference channels. This condition is sufficient for all and necessary for almost all channel matrices. Moreover, it applies to all channel topologies, i.e., to fully-connected channels as well as channels that have individual links absent, reflected by corresponding zeros in the channel matrix. Moreover, it captures the essence of interference alignment by virtue of being expressed in terms of a generic injectivity condition that guarantees separability of signal and interference. Finally, we provide codebook constructions achieving 1/2 degree of freedom for each user for all channel matrices satisfying the condition we identified.

show abstract

Degrees of freedom of interference channel with rank-deficient transfer matrix

Cited by 3 publications

References 16 publications