(Rate of LDPC) A binary block code that translates k message bits into codewords of length n is said to have rate R = k/n (which is k bits of information for every n transmitted binary digits. Shannon's theorem states that for R < C (where C is the capacity of the channel) and > 0, there is a code of some finite length n that attains rate R with a probability of error less than.
(a) Show that parity check matrix (6.3) is singular (mod 2).
(b) What is the rate of the LDPC code defined by parity check matrix (6.3)?