Hierarchical data recovery processing for extended product codes

A method includes distributively encoding data stored in a storage system using an erasure-correcting code. The encoded data is distributed into multiple w storage device arrays in the storage system. Each storage device array includes n storage devices. Each storage device is divided into m sectors or pages. The n storage devices are grouped into l groups of t storage devices each. Data erasures in the w storage device arrays are corrected by recovering erased data using the erasure-correcting code of un-erased data based on each row and column in each m×n array being protected by the erasure-correcting code for the data. Each group of t storage devices contains extra second responder parities to correct extra data erasures in addition to data erasures corrected by first responder vertical parities in each m×t subarray, and w, n, m, l and t are positive integers.