Coding for High-Density Recording on a 1-D Granular Magnetic Medium

• Published in: IEEE transactions on information theory Vol. 57; no. 11; pp. 7403 - 7417
• Main Authors: Mazumdar, A., Barg, A., Kashyap, N.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2011; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Channel capacity; Channel models; Channels; Combinatorial analysis; Encoding; Errors; Estimates; Focusing; Information theory; Lower bounds; Magnetic recording; Probabilistic logic; Probability distribution; Recording; Upper bound; Upper bounds
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2011.2158514

In terabit-density magnetic recording, several bits of data can be replaced by the values of their neighbors in the storage medium. As a result, errors in the medium are dependent on each other and also on the data written. We consider a simple 1-D combinatorial model of this medium. In our model, we assume a setting where binary data is sequentially written on the medium and a bit can erroneously change to the immediately preceding value. We derive several properties of codes that correct this type of errors, focusing on bounds on their cardinality. We also define a probabilistic finite-state channel model of the storage medium, and derive lower and upper estimates of its capacity. A lower bound is derived by evaluating the symmetric capacity of the channel, i.e., the maximum transmission rate under the assumption of the uniform input distribution of the channel. An upper bound is found by showing that the original channel is a stochastic degradation of another, related channel model whose capacity we can compute explicitly.