Improved and unified approximation for the BER of linear block codes

Claude Desset, Fabrice Labeau, Luc Vandendorpe, Benoît Macq

Abstract: In this paper, we provide an approximation for the BER achieved by using linear block error-correcting codes. Our work unifies and improves two anterior approximations, in the case of hard-decoding limited to the minimum distance of the code. We compare them to exact values for codes whose weight distribution is known. Our first improvement takes into account undecoded words, enabling the use of our approximation for all linear block codes, while the original ones were only accurate for perfect codes. A second improvement allows us to work in the large channel BER domain, by considering the binomial approximation of weight distributions. Previous approximations were not accurate, as asymptotic expressions based on low-weight error patterns do not hold when dealing with high BER values.