Erasure rate analysis and tighter upper bound for binary product codes

Enhanced Upper Bound for Erasure Recovery in SPC Product Codes

“…In the previous example of 16×16 SPCPC, it is difficult to distinguish our bound from the bound in [11]. This is because the bound in [11] does two opposite things.…”

“…This is not true because the terms are multiplicative rather than additive. The first enhancement to the bound in [11] is evident because we calculated e i up to i=7. For the case of M=N=5, Table 1 shows that for i=7 the average number of lost cells is 4.24 rather than 7.…”

“…In [11], although e i ≤ i, when evaluating the bound, making e i =i was assumed to have a minimal effect on the bound as compared to a large value of U i . This is not true because the terms are multiplicative rather than additive.…”

“…We have shown that unrecoverable patterns can be made without the basic square pattern. Pre-decoding erasure rate, p Post-decoding erasure rate, P Loose upper bound Upper bound in [6] Upper bound in [11] Enhanced upper bound Lower bound Monte carlo simulation…”

“…Moreover, the equations in [10] were derived for a specific matrix size and need to be extended before application to a larger matrix. Al-Shaikhi and Ilow [11], [12] avoided complexity and proposed a closed-form tight upper bound by analyzing the unrecoverable erasure patterns. Their analytical derivation was examined through computer simulation using Hamming and SPC product codes.…”