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Low implementation complexity, low-delay, and close-to-optimal performance of spatially-coupled LDPC codes over a wide variety of channels make them a very good candidate for upcoming wireless communication standards. However, due to the nature of the sliding window decoding architecture that is used to decode these codes, the associated error performance is considerably degraded over channels with memory, such as the burst erasure channel. In this case, using a block interleaver to break up the effects of the channel memory is not a viable option, since a block interleaver introduces a large amount of delay to the communication system and therefore takes back many of the advantages of using a sliding window decoder. In this paper, a reduced-delay communication system employing a convolutional interleaver is proposed. This scheme benefits from the inherent convolutional nature of the spatially-coupled codes and matches their structure with a low-delay convolutional interleaver. Thus, the resulting communication system exhibits very low overall delay. The performance of the proposed communication system is analyzed using the density evolution technique. Specifically, single-memory (minimum decoding delay), asymptotically (3,6)-regular spatially-coupled LDPC code ensembles are considered in the presence of burst erasures and the performance improvement of using a convolutional interleaver is demonstrated as a function of added interleaving delay in terms of iterative decoding thresholds.