Improved upper bound for erasure recovery in binary product codes

Product codes are powerful codes that can be used to correct errors and/or recover erasures. The focus of this paper is to evaluate the performance of such codes under the erasure scenarios. Judging the erasure recovery performance of a product code based on its minimum distance is pessimistic because the code is actually capable of recovering many erasure patterns beyond those with the number of erasures determined by the minimum distance. By investigating the non-correctable erasure patterns, this paper develops a tight upper bound on the post-decoding erasure rate for any binary product code. The analytical derivations are verified through computer simulations using Hamming and single parity check (SPC) product codes. A good agreement between the derived formulas and simulation results is documented.