In this paper, we introduce packet low-density parity-check (packet-LDPC) codes for high-density tape storage systems. We report on the performance of two error control code (ECC) architectures based on the packet-LDPC codes. The architectures are designed to be (approximately) compatible with the widely used ECMA-319 ECC standard based on two interleaved concatenated 8-bit Reed-Solomon (RS) codes. One architecture employs an inner RS code; the other employs an inner turbo product code with single parity-check constituent codes (TPC-SPC). Both employ a packet-LDPC code as the outer code. As for the ECMA-319 system, both schemes are required to correct noise bursts due to media defects and synchronization loss, as well as the loss of one of eight tracks (due to a head clog, for example). We show that the first packet-LDPC code architecture substantially outperforms the ECMA-319 scheme and is only a few tenths of a decibel inferior to a long, highly complex 12-bit RS scheme. The second architecture outperforms both the ECMA-319 and the long RS code scheme.