On Minimum-WER Performance of a Class of LDPC Codes for the BSC/E Under Extended Bounded-Distance Decoding

We study the word-error-rate (WER) performance and the WER-minimizing decision thresholds plusmnt* for the class of row-column-diagonal (RCD) array codes and their generalizations on the binary symmetric channel with erasures (BSC/E) where decoding is via an extended bounded-distance decoder (e-BDD). This model applies to very-high-data-rate systems where soft-decision iterative decoding is impractical. We demonstrate that substantial WER performance gain can be obtained, especially at higher channel signal-to-noise ratio (CSNR) (CSNR ₌Delta 10 log₁₀ (1/2sigma²)) values, by employing two optimal thresholds ( plusmnt*) chosen to minimize WER. We study the WER improvement and signal-to-noise ratio (SNR) performance gain as a function of code length (n) for fixed minimum distance (d_min), and as a function of (d_min) for fixed (n). A distinct difference in the behavior of WER versus the threshold t, and the optimal threshold t* versus SNR, is observed between codes with odd and even d_min, with the even d_min. codes exhibiting larger performance improvements when employing a BSC/E instead of a BSC