An Iteratively Decodable Tensor Product Code with Application to Data Storage

TL;DR

This paper introduces a tensor product error-correcting code with iterative decoding that achieves comparable or better performance than traditional LDPC codes while reducing decoding complexity, suitable for data storage applications.

Contribution

The paper proposes a novel tensor error-pattern correcting code (T-EPCC) with a low-complexity iterative decoding algorithm for improved data storage reliability.

Findings

T-EPCC-qLDPC achieves similar performance to single-level qLDPC with half the decoding complexity.

1 KB T-EPCC-qLDPC outperforms 1/2 KB single-level qLDPC at the same complexity.

The code is linear time encodable and suitable for large redundancy requirements.

Abstract

The error pattern correcting code (EPCC) can be constructed to provide a syndrome decoding table targeting the dominant error events of an inter-symbol interference channel at the output of the Viterbi detector. For the size of the syndrome table to be manageable and the list of possible error events to be reasonable in size, the codeword length of EPCC needs to be short enough. However, the rate of such a short length code will be too low for hard drive applications. To accommodate the required large redundancy, it is possible to record only a highly compressed function of the parity bits of EPCC's tensor product with a symbol correcting code. In this paper, we show that the proposed tensor error-pattern correcting code (T-EPCC) is linear time encodable and also devise a low-complexity soft iterative decoding algorithm for EPCC's tensor product with q-ary LDPC (T-EPCC-qLDPC). Simulation results show that T-EPCC-qLDPC achieves almost similar performance to single-level qLDPC with a 1/2 KB sector at 50% reduction in decoding complexity. Moreover, 1 KB T-EPCC-qLDPC surpasses the performance of 1/2 KB single-level qLDPC at the same decoder complexity.