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On the Sum-Capacity with Successive Decoding in Interference Channels

On the Sum-Capacity with Successive Decoding in Interference Channels,10.1109/ISIT.2011.6033790,Yue Zhao,Chee Wei Tan,Amir Salman Avestimehr,Suhas N.

On the Sum-Capacity with Successive Decoding in Interference Channels   (Citations: 1)
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In this paper, we investigate the sum-capacity of the two-user Gaussian interference channel with Gaussian su- perposition coding and successive decoding. We first examine an approximate deterministic formulation of the problem, and introduce the complementarity conditions that capture the use of Gaussian coding and successive decoding. In the deterministic channel problem, we show that the constrained sum-capacity oscillates as a function of the cross link gain parameters between the information theoretic sum-capacity and the sum-capacity with interference treated as noise. Furthermore, we show that if the number of messages of either user is fewer than the minimum number required to achieve the constrained sum- capacity, the maximum achievable sum-rate drops to that with interference treated as noise. We translate the optimal schemes in the deterministic channel model to the Gaussian channel model, and also derive two upper bounds on the constrained sum-capacity. Numerical evaluations show that the constrained sum-capacity in the Gaussian channels oscillates between the sum-capacity with Gaussian Han-Kobayashi schemes and that with single message schemes. I. INTRODUCTION We consider the sum-rate maximization problem in two- user Gaussian interference channels under the constraints of successive decoding. While the information theoretic capacity region of the Gaussian interference channel is still not known, it has been shown that a Han-Kobayashi scheme with random Gaussian codewords can achieve within 1 bit/s/Hz of the ca- pacity region (4). In this scheme, each user decodes both users' common messages jointly, and then decodes its own private message. In comparison, the simplest decoding constraint is treating the interference from the other users as noise. It has been shown that within a certain range of channel parameters for weak interference channels, treating interference as noise achieves the information theoretic sum-capacity (1), (6), (7). In this paper, we consider a decoding constraint — succes- sive decoding of Gaussian superposition codewords —t hat bridges the complexity between joint decoding (e.g. in Han- Kobayashi schemes) and treating interference as noise. We investigate the constrained sum-capacity and how to achieve it. To clarify and capture the key aspects of the problem, we resort to a deterministic channel model (2). In (3), the information theoretic capacity region for the two-user deterministic inter- ference channel is derived as a special case of the El Gamal- Costa deterministic model (5), and is shown to be achievable using Han-Kobayashi schemes. To capture the use of successive decoding of Gaussian codewords, we introduce the complementarity conditions on the bit levels in the deterministic formulation. We develop transmission schemes on the bit-levels, which in the Gaussian model corresponds to message splitting and power allocation of the messages. We then solve the constrained sum-capacity, and show that it oscillates (as a function of the cross link gain parameters) between the information theoretic sum-capacity and the sum-capacity with interference treated as noise. Fur- thermore, the minimum number of messages needed to achieve the constrained sum-capacity is obtained. We show that if the number of messages is limited to even one less than this minimum capacity achieving number, the sum-capacity drops to that with interference treated as noise. We then translate the optimal scheme in the deterministic interference channel to the Gaussian channel, using a rate constraint equalization technique. To evaluate the optimality of the translated achievable schemes, we derive two upper bounds on the sum-capacity with Gaussian Han-Kobayashi schemes, which automatically apply to the sum-capacity with successive decoding schemes. The two bounds are shown to be tight in different ranges of parameters. The remainder of the paper is organized as follows. Section II formulates the problem of sum-capacity with successive decoding of Gaussian codewords in Gaussian interference channels. Section III reformulates the problem with the de- terministic channel model, and then solves the constrained sum-capacity. Section IV translates the optimal schemes in the deterministic channel back to the Gaussian channel, and derives two upper bounds on the constrained sum-capacity. Conclusions are drawn in Section V. Due to space limitations, all the proofs are omitted here, and can be found in (9). II. PROBLEM FORMULATION IN GAUSSIAN CHANNELS
Conference: IEEE International Symposium on Information Theory - ISIT , vol. abs/1103.0, pp. 1494-1498, 2011
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    • ...Conclusions are drawn in Section V. Due to space limitations, all the proofs are omitted here, and can be found in [9]...
    • ...Complete solutions in asymmetric channels follow similar ideas. The details can be found in [9]...
    • ...We propose the following power allocation algorithm that equalizes the rate constraints, in which L counts the number of messages used by each user. The derivations can be found in [9]...
    • ...More specifically, the bounds are derived for the sum-capacity with Gaussian Han-Kobayashi schemes, which automatically upper bound the sum-capacity with successive decoding of Gaussian codewords, (as Gaussian superposition coding - successive decoding is a special case of Han-Kobayashi schemes [9])...
    • ...It is worth noting that although the above differences (1.8 bits and 1.0 bits) with SNR =3 0dB may not seem very significant, as SNR →∞ , both differences will go to infinity [9]...

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