Cyclic Codes Tailored to a Known Set of Error Patterns.
Jihoon Park, Jaekyun J. Moon · 2006
We propose a high-rate error-pattern control code based on a generator polynomial targeting a specific set of known dominant error patterns. This code is based on first constructing a low-rate cyclic code that possesses a distinct syndrome set for each target error pattern. This base code is then extended by simply applying the same generator polynomial to a larger message block. It is shown that the captured syndrome along with a soft metric can be used to correct a single occurrence of any target error pattern within the codeword with a high probability of accuracy. The proposed scheme outperforms, by a significant margin, conventional post-Viterbi error correction based on high- rate error detection coding. The performance comparison is provided for a high-density perpendicular recording model. I. INTRODUCTION Conventional block error correction codes (ECCs), such as the Bose-Chaudhuri-Hocquenghem (BCH) code, are designed to have a certain minimum distance property that guarantees correction of up to t errors within the received data word. In interference-dominant channels, such as high-density magnetic recording, errors tend to occur in specific patterns. While conventional codes can also correct some of these frequently observed error patterns, they are not very effective in providing immunity against these error patterns, some of which may have high weights. In this paper, we introduce a new approach to designing error control codes. Focusing on a cyclic code, we aim at correcting any single occurrence of L known error patterns, rather than t bit errors. Targeting a list of known dominant error patterns that make up a very large percentage of all observed occurrences of errors, we first construct a generator polynomial that can produce distinct syndrome sets for the targeted error patterns. No two error patterns within the list map to the same syndrome set, and the single occurrence of any targeted error patterns can be successfully detected. Among the target error patterns, the captured syndrome points uniquely to one error pattern and either its precise position or a few possible positions. By tailoring the generator polynomial specifically to the known set of error polynomials, the code becomes highly effective in handling the frequently observed error patterns. In the second step, the rate of the code is extended by simply applying the same generator polynomial to a considerably larger message block. To make the extended code cyclic, the overall code length is constrained to be an integer multiple of the base code length. The captured syndrome uniquely identifies an error pattern from the target list, but it can only point to a number of possible error-pattern positions. The final decision on the position is based on computing the maximum likelihood position, given the error pattern and a number of possible positions. A biased form of soft metric is also proposed that can help reduce the probability of mis- correction. Both bit error rate (BER) simulation results and analysis of sector error rate (SER) based on outer Reed-Solomon (RS) codes with varying byte-error correction capabilities are compared for the proposed error correction scheme as well as a conventional post-Viterbi error correction scheme under various mixed noise environments.