2024 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 57, NO. 7, JULY 2009 On Reliable Communications over Channels Impaired by Bursty Impulse Noise Dario Fertonani, Member, IEEE, and Giulio Colavolpe, Member, IEEE Abstract—Digital communications over channels impaired by impulse noise are addressed. We adopt a two-state Markov model that allows to describe the typical bursty nature of the impulse noise, in contrast to the memoryless models generally considered in the literature. For this channel, we evaluate the achievable information rate and propose a couple of practical communication systems based on powerful codes and iterative receivers. Moreover, we discuss the effectiveness of the considered receivers in terms of performance/latency tradeoff as well as in terms of robustness to erroneous channel estimations. The proposed schemes are shown to perform fairly close to the theoretical limits, and signiﬁcantly better than the conventional schemes employing memoryless detection. Index Terms—Impulse noise, Markov channels, maximum-a- posteriori symbol detection, achievable information rate, low- density parity-check codes. I. I NTRODUCTION T HE power delivery networks and some mobile radio sce- narios are often characterized by interference that exhibits a signiﬁcant impulsive nature and cannot be properly described by the conventional additive white Gaussian noise (AWGN) model. Such phenomena, referred to as “impulse noise”, are generally described by means of the Class-A model [1] or the Bernoulli-Gaussian model [2]. Since these models are memoryless, they cannot describe one of the main features of the actual channel, i.e., the occurrence of impulsive bursts (see [3] and references therein). Hence, given that the actual channel is characterized by a signiﬁcant amount of memory, it is interesting to evaluate which performance gain can be achieved when the memory is exploited in the system design, in terms of ultimate theoretical limits as well as performance of practical systems. To address these issues, we follow the guidelines in [3] and consider a channel model that modi- ﬁes the Bernoulli-Gaussian model [2] such that the channel state is, instead of a Bernoulli process, a two-state Markov process [4]. A two-state Markov process indeed provides a simple and effective way for describing a bursty evolution of the channel state [5]. The considered model, yet able to account for the actual channel memory, is still as manageable as the memoryless ones in [1], [2], so that we can derive an Paper approved by G. M. Vitetta, the Editor for Equalization and Fading Channels of the IEEE Communications Society. Manuscript received Decem- ber 11, 2007; revised August 17, 2008 and November 4, 2008. D. Fertonani is with Scuola Superiore Sant’Anna, Via G. Moruzzi 1, I- 56124 Pisa (e-mail: dario.fertonani@gmail.com). G. Colavolpe is with the Department of Information Engineering, Uni- versity of Parma, Viale G. P. Usberti 181/A, 43100 Parma, Italy (e-mail: giulio@unipr.it). Parts of this work appear in the proceedings of the IEEE International Symposium on Power Line Communications and its Applications (ISPLC 2008) and the IEEE International Conference on Communications (ICC 2008). Digital Object Identiﬁer 10.1109/TCOMM.2009.07.070638 algorithm for optimal maximum-a-posteriori (MAP) symbol detection. We ﬁrst carry out an information-theoretical analysis on the performance limits imposed by the channel, in terms of information rate [6] of systems employing linear modulations. Although the state process underlying the channel is the same as in the Gilbert-Elliott model (see [5] and references therein), whose information rate can be analytically computed [5], the same analytical arguments do not lead to a closed-form expression here, since the channel-output alphabet is not ﬁnite nor discrete [7]. Hence, we compute the information rate by means of the simulation-based method described in [8], exploiting the derived algorithm for MAP symbol detection. Such investigations deﬁnitely show that the ultimate perfor- mance limit improves as the memory of the impulse noise becomes more signiﬁcant, motivating us to design practical schemes able to exploit the channel memory. Moreover, we compare the information rate achievable in conditions of ideal channel estimation with that achievable in conditions of mismatched decoding [9], that is, with errors in the channel estimation. Interestingly, the system results fairly robust to possible estimation errors. Aimed at approaching the theoretical performance limits as close as possible, we focus on systems employing powerful channel codes, such as low-density parity-check (LDPC) codes or turbo-like codes [10], [11], and propose two receivers based on MAP detection. One receiver exploits the exchange of soft information between the MAP detector and the decoder, as in the turbo-equalization schemes [12], while the other receiver is simpler and does not perform iterative detection. We show that both receivers can perform close to the ultimate limit, and signiﬁcantly better than the conventional schemes that neglect the channel memory. The remainder of this paper is organized as follows. In Section II, we describe the considered channel model and compare it with the Bernoulli-Gaussian model. In Section III, we derive an algorithm for optimal MAP symbol detection, which is then exploited for the evaluation, in Section IV, of the achievable information rate. In Section V, we describe a couple of practical communication schemes, comparing their performance and complexity. Finally, some conclusions are drawn in Section VI. II. CHANNEL MODEL A sequence of M -ary complex-valued symbols {c k } K k=1 belonging to a suitable constellation, e.g., phase-shift key- ing (PSK) or quadrature amplitude modulation (QAM), is transmitted over a discrete-time channel that introduces ad- 0090-6778/09$25.00 c  2009 IEEE