The background description provided herein is for the purpose of generally presenting the context of the disclosure. Work of the presently named inventor(s), to the extent the work is described in this background section, as well as aspects of the description that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art against the present disclosure.
In information theory, a noisy channel coding theorem establishes that for any given degree of noise contamination of a communication channel, it is possible to communicate discrete data, approximately error free, at a determinable maximum rate through the channel. The maximum rate of approximately error free transmission through the channel is expressed as a function of bandwidth and a signal-to-noise ratio (SNR). Furthermore, the noisy channel coding theorem describes the maximum possible efficiency of error correcting methods versus the levels of noise interference and data corruption.
A low density parity check (LDPC) code is a linear error correcting code designed to overcome noise. LDPC codes are associated with LDPC code words that are defined by a sparse parity-check matrix. This sparse parity-check matrix is often randomly generated, subject to scarcity constraints. LDPC code words have a fixed number of symbols that form a full code word. However, input data may have fewer symbols than a requisite number of symbols of a full code word. The requisite number of symbols may be based on the hard disk drive sector size. Accordingly, different models, series, and manufacturers may have numerous code words. Since the numerous code words are different, encoders and decoders must be compatible with various codes. Therefore, while the LDPC codes seek to overcome noise, using a requisite number of symbols and the overhead of maintaining numerous codes reduces the adaptability of LDPC codes for different storage mediums.