On LDPC codes for Gaussian interference channels

Abstract

Abstract—In this paper, we focus on the two-user Gaussianinterference channel (GIC), and study the Han-Kobayashi (HK)coding/decoding strategy with the objective of designing low-density parity-check (LDPC) codes. A code optimization algo-rithm is proposed which adopts a random perturbation techniquevia tracking the average mutual information. The degree distri-bution optimization and convergence threshold computation arecarried out for strong and weak interference channels, employingbinary phase-shift keying (BPSK). Under strong interference, itis observed that optimized codes operate close to the capacityboundary. For the case of weak interference, it is shown that viathe newly designed codes, a nontrivial rate pair is achievable,which is not attainable by single user codes with time-sharing.Performance of the designed LDPC codes are also studied forfinite block lengths through simulations of specific codes pickedfrom the optimized degree distributions. I. I NTRODUCTION Full characterization of the capacity region of the two-userGIC is an open problem for the general case, and only innerand outer bounds are available in the literature. The bestreported achievable rate region to date is due to Han andKobayashi (HK) [1]. Despite the superiority of the rate region,there is no work on exploring explicit and implementablechannel codes adopting this coding and decoding schemein the current literature. With this motivation, in this paper,we study the design and performance of low-density parity-check (LDPC) over GICs utilizing the HK strategy.In the current literature, LDPC codes have been successfullyoptimized for multi-user channels, where promising resultsare obtained for the two-user equal gain multiple-access-channel (MAC) [2], Gaussian broadcast channel [3], relaychannel [4], and symmetric two-user GIC [5] where identicaldistributions for both messages are used without employingthe HK coding/decoding strategy. In this paper, we investigatethe performance of irregular LDPC codes over the two-userGIC employing the HK coding/decoding scheme with fixedchannel gains and finite constellations. In the proposed HKscheme information of each transmitter is split into privateand public parts which are encoded using separate LDPCcodes. The encoded bits are mapped to specific constellationpoints and the resulting signals are superimposed to generatethe transmitted signal. At the receiver side, public messagesand private message of the intended user are decoded con-currently utilizing an iterative joint decoder. It is shown thatthe proposed joint decoder enjoys a symmetry property ofthe exchanged soft information which plays a key role insimplifying the mutual information calculations.A code optimization algorithm is proposed based on randomperturbations. The algorithm can be considered as a specificinstance of differential evolution technique of [6], whichis a robust and effective method. The optimization stepsthrough random perturbations starting from admissible degreedistributions [5]. The convergence of ensembles is verifiedby tracking the mutual information evolution utilizing Monte-Carlo simulations.Computation of HK achievable rate region is prohibitivelydifficult since full characterization of the rate region requiresoptimization over numerous random variables with large car-dinalities. Therefore, in this paper, instead of computing theentire region, a subregion [7] is computed with a smallercomplexity, where a finite number of power allocations areconsidered and no time sharing (TS) is utilized.Having implemented the HK strategy, we carry out thecode optimization for the two-user GIC through examplesconsidering strong and weak interference. For comparisonpurposes we will use single user codes with TS implementedwith two different power constraints. The first one is naiveTS motivated by practical limitations on the power amplifiers,for which we have individual power constraints for the twousers for each transmitted symbol. The second one is non-naive TS where the users can “pool” their power resourcesand increase their individual power levels for certain fractionof the transmission while keeping the total average powerover the entire codeword under a certain value [8]. Promisingresults are obtained under strong interference, where a ratepair very close to the capacity boundary is achieved. Underweak interference, it is demonstrated that a non-trivial point,which is not achievable with the point-to-point (p2p) codeused with TS, is attainable. In our examples, we also evaluateand compare the performance of optimal p2p codes with theones optimized for the GIC, and demonstrate that significantimprovements are possible. We also provide simulation resultswith specific finite-length codes picked from the optimizedcode ensembles.The rest of the paper is organized as follows. In Section II,system model of the two-user GIC is described. In Section III,HK coding and decoding schemes are explained. In SectionIV, the proposed code optimization algorithm is described. InSection V, performance of p2p and optimized LDPC codesare investigated, where finite block length code simulationsare also included. Finally, Section VI concludes the paper.