Globecom 24 Worksho - Emerging Technologies for 5G Wireless Cellular Networks Interference Management via Sliding-Window Suerosition Coding Hosung ark, Young-Han Kim, Lele Wang University of California, San Diego La Jolla, CA 9293, USA Email: {hark,yhk,lew}@ucsd.edu Abstract The sliding-window suerosition coding scheme achieves the erformance of simultaneous decoding with ointto-oint channel codes and low-comlexity decoding. This aer rovides a case study of how this concetual coding scheme can be transformed to a ractical coding technique for two-user Gaussian interference channels. Simulation results demonstrate that sliding-window suerosition coding can sometimes double the erformance of the conventional method of treating interference as noise, still using the standard LTE turbo codes. I. INTODUCTION For high data rates and massive connectivity, the nextgeneration cellular networks are exected to deloy many small base stations. While such dense deloyment rovides the benefit of bringing radio closer to end users, it also increases the amount of interference from neighboring cells. Consequently, smart management of interference would become one of the key enabling technologies for high-sectral-efficiency, low-ower, broad-coverage wireless communication. Over the ast decades, several techniques at different rotocol layers have been roosed to mitigate adverse effects of interference in wireless networks; see, for examle, [] [3]. One imortant concetual technique at the hysical layer is simultaneous decoding [4], [5], whereby each receiver decodes for the desired signal as well as art or whole of interference. When interference is strong [6], [7], this simultaneous decoding technique achieves the otimal erformance for the twouser Gaussian interference channel using good oint-to-oint codes. Moreover, it achieves the otimal maximum likelihood decoding erformance in general, when the encoders are restricted to oint-to-oint random code ensembles [8], [9]. The celebrated Han-Kobayashi coding scheme [], which achieves the best known erformance for general two-user interference channels, also uses simultaneous decoding as a crucial comonent. As a main drawback, however, each receiver in simultaneous decoding has to emloy some form of multiuser sequence detection, which usually requires high comutational comlexity to imlement. This issue has been tackled lately by a few aroaches [], [2] based on emerging satially couled [3] and olar [4] codes, but these solutions require the develoment of new families of codes (instead of using conventional oint-to-oint channel codes This work was suorted in art by the National Science Foundation under Grant CCF-32895. such as LDC codes [5] and turbo codes [6]) and involve very long block lengths. For this reason, most existing communications systems, which use conventional oint-to-oint channel codes, treat interference as noise. While this simle scheme can achieve good erformance with low comutational comlexity when interference is weak [7] [9], the erformance degrades as interference becomes stronger, which is often the case for dense wireless networks. In articular, in the high signal-tonoise ratio/interference-to-noise ratio limit, the erformance of treating interference as noise has an unbounded ga from that of simultaneous decoding. ecently, the sliding-window suerosition coding scheme was roosed [2] that achieves the theoretical erformance of simultaneous decoding with oint-to-oint channel codes and low-comlexity decoding. This scheme is built on basic comonents of network information theory, combining the ideas of block Markov coding and sliding-window decoding (commonly used for multiho relaying and feedback communication, but not for single-ho communication) and suerosition coding and successive cancellation decoding (allowing low-comlexity decoding with oint-to-oint codes). In this aer, we investigate the erformance of slidingwindow suerosition coding (SWSC) for the two-user Gaussian interference channel and demonstrate that SWSC rovides a feasible solution to achieve the erformance of simultaneous decoding with existing oint-to-oint codes. We first evaluate the theoretical erformance of SWSC under modulation constraints and comare it with the erformance of treating interference as noise and simultaneous decoding. As is fully described in Section III, SWSC tracks the erformance of simultaneous decoding when interference is moderate to strong. To further test the feasibility of SWSC, we then translate the concetual coding scheme behind the theoretical erformance to a ractical imlementation based on actual turbo codes used in the LTE standard [2]. In Section IV, we show that our imlementation achieves the erformance guaranteed by the theory, even when the block length is relatively short (248). In articular, our imlementation outerforms conventional systems that treat interference as noise when interference is moderate to strong. In the next section, we begin our discussion by reviewing the basic oerations of SWSC [2] for the secial case of the two-user Gaussian interference channel. 978--4799-747-2/4/$3. 24 IEEE 972
Globecom 24 Worksho - Emerging Technologies for 5G Wireless Cellular Networks II. SLIDING-WINDOW SUEOSITION CODING FO THE GAUSSIAN INTEFEENCE CHANNEL The two-user Gaussian interference channel is defined as Y = g X + g 2 X 2 + Z, Y 2 = g 2 X + g 22 X 2 + Z 2. Here, X i 2 X n, i =, 2, is a transmitted signal from sender i with average ower constraint i, where n is the block length and Y i 2 n is a received signal at receiver i, and Z i 2 n N(, ), i =, 2, are noise comonents. We assume that each receiver i knows local channel gain coefficients g ij 2, j =, 2, from both senders, which are held fixed during the communication. The block diagram of this channel is shown in Fig.. () where U(j), V (j), and W (j) 2 {, +} n are BSK signals. Fig. 2 reresents the suerosition coding with U and V for X. U V W Y Y Fig. 2. Suerosition coding with virtual inut signals U, V, and W. Fig.. The two-user Gaussian interference channel. Sliding-window suerosition coding (SWSC) [2] is based on several basic building blocks in network information theory such as suerosition coding [22], block Markov coding [23], [24], successive cancellation decoding [22], [25], [26], and sliding-window decoding [27] [29]. Sender i encodes its messages by using suerosition coding with multile suerimosed layers and block Markov coding throughout multile blocks. eceiver i erforms successive cancellation decoding of all suerimosed layers from sender i and some suerimosed layers from the other sender within a window length according to a redetermined decoding order and slides the decoding window until it reaches the end of blocks. We now elaborate the encoding/decoding rocess of the secific version of SWSC considered in this aer. For block j =,...,b, let m i (j) 2 {, 2,...,2 nri } be the message to be communicated from sender i to receiver i. Similarly, let X i (j), Y i (j), and Z i (j) be the channel inut, outut, and noise for sender/receiver i in block j. The original SWSC allows for full flexibility in the number of suerimosed layers, the number and structure of auxiliary random variables for suerosition coding, and the decoding order. Here, we limit our attention to two layers of BSK signals that form a 4-AM signal by suerosition and a fixed decoding order. In articular, X (j) = U(j)+ V (j), X 2 (j) = 2 W (j), Y Y (2) The encoding and decoding oerations are deicted in Fig. 3. The signal U(j) carries the message m (j ) from the revious block, and V (j) and W (j) carry m (j) and m 2 (j), resectively, from the current block. By convention, we set m () = m (b) =. The arameter determines the ratio of owers slit into U(j) and V (j). Throughout this aer, =.8, which makes X 2 { 3 / 5, / 5, + / 5, +3 / 5} a uniformly-saced 4-AM signal. The corresonding channel oututs are Y (j) =g U(j)+g V (j) + g 2 2 W (j)+z (j), Y 2 (j) =g 2 U(j)+g2 V (j) + g 22 2 W (j)+z 2 (j). At the end of block j +, receiver first decodes Y (j) and Y (j + ) to recover m (j) carried by V (j) and U(j + ). Note that U(j) and W (j) are already known from the revious decoding window and thus the effective channel outut from Y (j) is g V (j)+z (j). This decoding ste is successful if r ale I(U; Y )+I(V ; Y U, W ). (3) eceiver then decodes Y (j+) to recover m 2 (j+) carried by W (j +), where U(j +) is known from the first ste and V (j + ) is interference. This decoding ste is successful if r 2 ale I(W ; Y U). (4) At the end of block j +, receiver 2 first decodes Y 2 (j) and Y 2 (j + ) to recover m (j) carried by V (j) and U(j + ), where U(j) is known from the revious decoding window and V (j) is interference. eceiver 2 then decodes Y 2 (j) to recover m 2 (j) carried by W (j), where U(j) and V (j) are already known. These decoding stes are successful if r ale I(U, V ; Y 2 ), (5) r 2 ale I(W ; Y 2 U, V ). (6) 973
Globecom 24 Worksho - Emerging Technologies for 5G Wireless Cellular Networks block U m m m m m m V m m m m m m W m m m m m m m decoding at receiver decoding at receiver 2 Fig. 3. The encoding and decoding oerations for b =7blocks. The message m (2) is carried by signals V (2) and U(3) (shaded in blue), while the message m 2 (5) is carried by W (5) (shaded in red). The sliding-window decoding of m (2) at receiver is based on its received signals Y (2) and Y (3) over two blocks. eceiver first recovers m (2) (equivalently, V (2) and U(3)) and then recovers m 2 (3) (equivalently, W (2)). The signals U(2) and W (2) are already known from the revious decoding window (shaded in gray). eceiver 2 oerates slightly differently by recovering first m (5) from and then m 2 (5) based on two blocks Y (5) and Y (6). At the end of the last block j = b, receiver 2 addtionally decodes Y 2 (b) to recover m 2 (b) carried by W (b), which is again successful if (6) holds. Since m (),...,m (b ) and m 2 (),...,m 2 (b) are sent over b blocks, the actual rate for sender/receiver is = r (b )/b and the actual rate for sender/receiver 2 is 2 = r 2. Combining these results (4) (6), we can asymtotically achieve the following rate region with SWSC: ale min{i(u; Y )+I(V ; Y U, W ),I(U, V ; Y 2 )}, 2 ale min{i(w ; Y U),I(W ; Y 2 U, V )}, where U, V, and W are indeendent Unif{, +} random variables. III. THEOETICAL EFOMANCE COMAISON In this section, we consider treating interference as noise and simultaneous decoding for the channel model in () and comare the theoretical erformance of SWSC to them. A. Treating Interference as Noise The achievable rate region of treating interference as noise is characterized by ale I(X ; Y ), (8) 2 ale I(X 2 ; Y 2 ), where X is Unif{ 3 / 5, / 5, + / 5, +3 / 5} and X 2 is Unif{ 2, + 2 } as in (2). Note that the receivers here use the constellation (modulation) information of interference instead of the simle signal-tointerference-noise ratio (SIN) metric, but they do not decode for the interference codewords. B. Simultaneous Nonunique Decoding In simultaneous decoding, each receiver recovers codewords from both senders. Here we consider a variant called simultaneous nonunique decoding, which rovides an imroved erformance by disregarding the uniqueness of the interference codeword [3]. The achievable rate region of simultaneous nonunique decoding is characterized by ale I(X ; Y X 2 ), 2 ale I(X 2 ; Y 2 X ), (9) + 2 ale min{i(x,x 2 ; Y ),I(X,X 2 ; Y 2 )}, (7) where X and X 2 are again given as in (2). Note that simultaneous nonunique decoding achieves the caacity region when interference is strong, that is, g 2 2 g 2 and g 2 2 g 2 22. C. Comarison with SWSC We demonstrate the theoretical erformance of slidingwindow suerosition coding () comared to the theoretical erformance for simultaneous nonunique decoding () and treating interference as noise (). In the original SWSC scheme, the auxiliary signals U, V, and W as well as the suerosition maing x (u, v) can be chosen otimally, which guarantees that is identical to. In our setting, however, we have restricted the auxiliary signals to be BSK so that X is uniformly-saced 4- AM. Therefore, it is a riori unclear whether would be close to. For simlicity, assume the symmetric rate, ower, and channel gains, that is, = 2 =, = 2 =, g = g 22 =, and g 2 = g 2 = g. We control signalto-noise ratio (SN) and interference-to-noise ratio (IN) by varying transmit ower and find the minimum ower that achieves the given rate for,, and. The lots of the minimum symmetric transmit ower vs. the achievable symmetric rate are shown in Fig. 4 for g =.9,.,.,.2. Note that the ga between and is due to the subotimal choice of U and V under our modulation constraints. Nonetheless, aroaches and significantly outerforms in high SN. IV. IMLEMENTATION WITH LTE TUBO CODES To imlement SWSC with oint-to-oint channel codes, we use a binary linear code of length 2n and rate r /2 for [V (j) U(j+)] as U(j+) and V (j) carry m (j) in common. Similarly, we use a binary linear code of length n and rate r 2 for W (j) to carry m 2 (j). We adot the turbo codes used in the LTE standard [2], which allow flexibility in code rate and block length. In articular, we start with the rate /3 mother code and adjust the rates and lengths according to the rate matching algorithm in the standard. Note that for r < 2/3, some code bits are reeated and for r > 2/3, some code bits are unctured. To evaluate the erformance of SWSC, the block length n and the number of blocks b are set to 248 974
Globecom 24 Worksho - Emerging Technologies for 5G Wireless Cellular Networks.9.8.9.8.3.3.2.2.. 2 3 4 5 6 7 8 9 (a) g =.9 2 3 4 5 6 7 8 9 (b) g =..9.8.9.8.3.3.2.2.. 2 3 4 5 6 7 8 9 (c) g =. 2 3 4 5 6 7 8 9 (d) g =.2 Fig. 4. The transmit ower vs. achievable symmetric rate for the symmetric Gaussian interference channel. and 2, resectively. We use the LOG-MA algorithm for the turbo decoding with the maximum number of iterations set to 8 for each stage of decoding. We assume that a rate air (, 2 ) is achieved for given i and g ij if the resulting bit-error rate (BE) is below 3 over indeendent sets of simulations. We first consider the symmetric case studied in the revious section. Our simulation results are overlaid in Fig. 4 along with the theoretical erformance curves. It can be checked that the erformance of our imlementation,, tracks the theoretical erformance of, confirming the feasibility It should be stressed that b is the total number of blocks, not the size of the decoding window (which is 2). Every message is recovered with oneblock delay. While a larger b reduces the rate enalty of /b, it also incurs error roagation over multile blocks, both of which were roerly taken into account in our rate and BE calculation. of sliding-window suerosition coding. Note that outerforms in high SN. ecall that the latter is the theoretical erformance bound of treating interference as noise, whose actual erformance (under a fair comarison) would be even worse. As another feasibility test, we consider the Gaussian fading interference channel, where g ij are i.i.d. N(, ). We indeendently generate 25 sets of channel gain coefficients, in order to evaluate the erformance of SWSC under various channel conditions. We calculate the average minimum ower avg over the 25 channel realizations for =.3,,,. As shown in Fig. 5, is very close to, which is tracked by the actual imlementation. Note that is consistently better than, with the ga becoming larger in high rate/high SN regime. 975
Globecom 24 Worksho - Emerging Technologies for 5G Wireless Cellular Networks.8.3.2. 5 5 2 25 3 35 4 45 avg Fig. 5. The average transmit ower vs. achievable symmetric rate for the Gaussian interference channel with random coefficients. V. CONCLUDING EMAKS While there should be more extensive studies on its feasibility, the results in this aer indicate that the sliding-window suerosition coding (SWSC) scheme has some otential as a ractical channel coding technique for interference management. We remark on two directions in imroving the current imlementation. First, the decoding orders at the receivers can be further otimized; for examle, SWSC can always achieve the erformance of treating interference as noise under certain decoding orders. Second, the structure of the suerosition maing can be further otimized, esecially, by the ower ratio control ( 6=.8). EFEENCES [] G. Boudreau, J. anicker, N. Guo,. Chang, N. Wang, and S. Vrzic, Interference coordination and cancellation for 4G networks, IEEE Commun. Mag., vol. 47, no. 4,. 74 8, Ar. 29. [2] C. Seol and K. Cheun, A statistical inter-cell interference model for downlink cellular OFDMA networks under log-normal shadowing and multiath ayleigh fading, IEEE Trans. Commun., vol. 57, no.,. 369 377, Oct. 29. [3] V. Cadambe and S. Jafar, Interference alignment and degrees of freedom of the K-user interference channel, IEEE Trans. Inf. Theory, vol. 54, no. 8,. 3425 344, Aug. 28. [4] A. El Gamal and Y.-H. Kim, Network Information Theory. Cambridge, MA: Cambridge University ress, 2. [5] S. S. Bidokhti, V. M. rabhakaran, and S. N. Diggavi, Is non-unique decoding necessary? in roc. IEEE Int. Sym. Inf. Theory, Boston, MA, Jul. 22. [6] M. H. M. Costa and A. El Gamal, The caacity region of the discrete memoryless interference channel with strong interference, IEEE Trans. Inf. Theory, vol. 33, no. 5,. 7 7, May 987. [7] H. Sato, On the caacity region of a discrete two-user channel for strong interference, IEEE Trans. Inf. Theory, vol. 24, no. 3,. 377 379, May 978. [8] A. S. Motahari and A. K. Khandani, To decode the interference or to consider it as noise, IEEE Trans. Inf. Theory, vol. 57, no. 3,. 274 283, Mar. 2. [9] F. Baccelli, A. El Gamal, and D. N. C. Tse, Interference networks with oint-to-oint codes, IEEE Trans. Inf. Theory, vol. 57, no. 5,. 2582 2596, May 2. [] T. S. Han and K. Kobayashi, A new achievable rate region for the interference channel, IEEE Trans. Inf. Theory, vol. 27, no.,. 49 6, Jan. 98. [] A. Yedla,. Nguyen, H. fister, and K. Narayanan, Universal codes for the gaussian mac via satial couling, in roc. 49th Ann. Allerton Conf. Comm. Control Comut., 2,. 8 88. [2] L. Wang and E. Sasoglu, olar coding for interference networks, rerint. [Online]. Available: htt://arxiv.org/abs/4.7293 [3] S. Kudekar, T. J. ichardson, and. L. Urbanke, Threshold saturation via satial couling: Why convolutional LDC ensembles erform so well over the BEC, IEEE Trans. Inf. Theory, vol. 57, no. 2,. 83 834, Feb. 2. [4] E. Arıkan, Channel olarization: A method for constructing caacityachieving codes for symmetric binary-inut memoryless channels, IEEE Trans. Inf. Theory, vol. 55, no. 7,. 35 373, Jul. 29. [5]. G. Gallager, Low Density arity Check Codes. Cambridge, MA: MIT ress, 963. [6] C. Berrou, A. Glavieux, and. Thitimajshima, Near Shannon limit errorcorrecting coding and decoding: Turbo codes, in roc. IEEE Int. Conf. Commun., Geneva, Switzerland, May 993,. 64 7. [7] X. Shang, G. Kramer, and B. Chen, A new outer bound and the noisyinterference sum-rate caacity for Gaussian interference channels, IEEE Trans. Inf. Theory, vol. 55, no. 2,. 689 699, Feb. 29. [8] V. S. Annaureddy and V. V. Veeravalli, Gaussian interference networks: Sum caacity in the low interference regime and new outer bounds on the caacity region, IEEE Trans. Inf. Theory, vol. 55, no. 7,. 332 35, Jul. 29. [9] A. S. Motahari and A. K. Khandani, Caacity bounds for the Gaussian interference channel, IEEE Trans. Inf. Theory, vol. 55, no. 2,. 62 643, Feb. 29. [2] L. Wang, E. Sasoglu, and Y.-H. Kim, Sliding-window suerosition coding for interference networks, in roc. IEEE Int. Sym. Inf. Theory 24, Jul. 24,.2749 2753. [2] 3G TS 36.22: Multilexing and channel coding, elease 2, 23. [22] T. M. Cover, Broadcast channels, IEEE Trans. Inf. Theory, vol. 8, no.,. 2 4, Jan. 972. [23] T. M. Cover and A. El Gamal, Caacity theorems for the relay channel, IEEE Trans. Inf. Theory, vol. 25, no. 5,. 572 584, Se. 979. [24] T. M. Cover and C. S. K. Leung, An achievable rate region for the multile-access channel with feedback, IEEE Trans. Inf. Theory, vol. 27, no. 3,. 292 298, 98. [25]. Ahlswede, Multiway communication channels, in roc. Int. Sym. Inf. Theory, Tsahkadsor, Armenian SS, 97,. 23 52. [26] H. H. J. Liao, Multile access channels. h.d. thesis, University of Hawaii, Honolulu, HI, 972. [27] A. B. Carleial, Multile-access channels with different generalized feedback signals, IEEE Trans. Inf. Theory, vol. 28, no. 6,. 84 85, Nov. 982. [28] L.-L. Xie and.. Kumar, An achievable rate for the multile-level relay channel, IEEE Trans. Inf. Theory, vol. 5, no. 4,. 348 358, Ar. 25. [29] G. Kramer, M. Gastar, and. Guta, Cooerative strategies and caacity theorems for relay networks, IEEE Trans. Inf. Theory, vol. 5, no. 9,. 337 363, Se. 25. [3] B. Bandemer, A. El Gamal, and Y.-H. Kim, Otimal achievable rates for interference networks with random codes, rerint. [Online]. Available: htt://arxiv.org/abs/2596 976