• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.37 no.3A
• /
• pp.151-156
• /
• 2012

In this paper, design of quasi-cyclic(QC) low-density parity-check codes is proposed to have full diversity for space-time bit-interleaved coded modulation(ST-BICM) systems. Necessary and sufficient conditions that the proposed scheme has full diversity are proved as the condition that submatrices corresponding to the system part of codewords are invertible. And new construction method of binary invertible matrices for QC LDPC codes in ST-BICM systems are also proposed and modification for parity-check matrices are also explained.

• Journal of the Chungcheong Mathematical Society
• /
• v.14 no.1
• /
• pp.21-28
• /
• 2001

In this paper we show that the following results remain valid for arbitrary Jordan derivations as well: Let d be a derivation of a complex Banach algebra A. If $d^2(x){\in}rad(A)$ for all $x{\in}A$, then we have $d(A){\subseteq}rad(A)$ ([5, p. 243]), and in a case when A is unital, $d(A){\subseteq}rad(A)$ if and only if sup{$r(z^{-1}d(z)){\mid}z{\in}A$ invertible} < ${\infty}$([3]), where rad(A) stands for the Jacobson radical of A, and r(${\cdot}$) for the spectral radius.