Optimal Data Decoding Strategies for Product-Coded Sequential Media Recording Via Latin Squares

In sequential media recording, such as found in tape data storage, data are typically accessed by reading signals from the beginning to the end of the recording medium in a streaming mode, which makes it unsuitable for random write accesses. However, sequential media is usually the preferred method for cold data storage in long-term data retention scenarios. In this study, we propose to increase the durability of sequential media by encoding data with locally recoverable codes (LRCs) both within and across different storage units creating a multidimensional product code external to the product code already implemented in the hardware. This way, local LRCs provide protection across the medium, whereas the LRCs spanning across different cartridges will provide global protection, which requires multiple drives and cartridges to help with the local decoding. Since global decoding is extremely costly, we require data allocation strategies that would use library resources efficiently. More specifically, we propose optimal data decoding and allocation strategies that would ensure minimum repair latency/communication cost in a global decoding setting for a given data request when local data reconstruction is not an option. We furthermore conduct analysis to find closed-form expressions and/or bounds on the overall latency/communication cost for product-coded systems under maintenance.