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 $\pm t^{\ast}$ 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) ($\hbox{CSNR}\triangleq 10\log_{10} (1/2\sigma^{2})$) values, by employing two optimal thresholds $(\pm t^{\ast})$ 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 $t^{\ast}$ 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.