In data storage, error correction coding (ECC) is used to achieve very high data integrity. For example, magnetic tape storage products are designed to ensure bit error rates in the range of 10−17 to 10−20 under normal operating conditions. Linear block codes such as Reed–Solomon (RS) codes and low-density parity-check (LDPC) codes are usually being employed in data storage products.

In optical and magnetic tape storage, powerful product codes are used to mitigate bad channel conditions that give rise to errors. Product codes allow the construction of very long block codes that are based on short constituent codes.

The resulting product code is not the best possible long code for a given dimension and a given length. However, since the code is composed of smaller component block codes, the complexity of decoding product codes becomes manageable in practice.

The burst-error performance of tape storage systems protected by product codes can be assessed based on two measures. First, the maximum lateral width of an erroneous stripe which can still be corrected is known as the dead-track correction capability.

Second, the maximum longitudinal width of an erroneous stripe that can still be corrected is useful in assessing the robustness of tape storage systems against instantaneous tape speed variations. An RS(64,54) code has been used as the column code of the product codes used in the first four LTO generations.

We are studying higher-rate column codes, which provide the same overall error-rate performance and have similar dead-track correction capability. Such higher rate codes allow the storage of more data on the tape cartridge at the same error correction capability.

In tape storage, a fixed-size data set, which is to be written on tape, consists of several sub data sets where each sub data set is protected by N-byte-interleaved product codes. The layout of a written data set on tape is such that the rows of any particular sub data set are spaced as far apart as possible to mitigate spatial burst errors on tape.

Figure 1 indicates the protection that can be achieved by proper subdata set placement with deep interleaving. Moreover, in conventional tape storage systems including LTO tape systems, headers are protected by an interpolation scheme that is inefficient in terms of required rewrite area. We are designing novel error correction schemes to increase robustness against header errors.

We are exploring the potential applicability of novel coding techniques to magnetic recording. For instance we have extended the principle of reverse concatenation (RC) to tape and proposed a new capacity-efficient RC scheme with a modulation code having less than 1% redundancy [2008-3].

This new format supports novel ECC techniques based on turbo and low-density parity-check (LDPC) codes. Innovative code design techniques and the theory of iterative decoding have made significant progress in the past few years moving signal-to-noise ratio (SNR) gains very close to the theoretical limit. However, these techniques are still in their infancy in terms of implementation.

Data layout on tape with deep interleaving

Figure 1. Data layout on tape with deep interleaving.

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Mark A. Lantz

Mark A. Lantz

IBM Research scientist