The weight distributions of some product codes

Abstract

General expressions a r e derived far t h e weight distributions of t h e binary product codes S,, @ Sm, Em1 @ Sm, 9 a n d Em1 @ Zm, , where S, is t h e [2, -lrm,2m-1] simplex code, ' R , is t h e [2", m + 1, 2,-' ] first order Reed Muller code, a n d & ,is t h e [m, m -1,2] even weight code.Rm, @ RmZ Sm, @ Rm,

Performance characteristics and weight distribution analysis of turbo product code with Reed–Muller component codes

“…Figs. [10][11][12][13] show that the cdf distribution approaches the Gaussian cdf distribution as the code length increases. …”

“…The weight distribution of higherorder RM codes and most families of product codes are unknown in general [7,10]. In this paper, the weight distribution of various RM codes of different lengths and TPCs with first-order RM component codes are obtained and analyzed for their good performance.…”