  Digital data transfer can be protected by means of suitable error correcting
codes. Among the families of state-of-the-art codes, LDPC (Low Density
Parity-Check) codes have received a great deal of attention recently, because
of their performance and flexibility of operation, in wireless and mobile radio
channels, as well as in cable transmission systems. In this paper, we present a
class of rate-adaptive LDPC codes, obtained as properly punctured simplex
codes. These codes allow for the use of an efficient soft-decision decoding
algorithm, provided that a condition called row-column constraint is satisfied.
This condition is tested on small-length codes, and then extended to
medium-length codes. The puncturing operations we apply do not influence the
satisfaction of the row-column constraint, assuring that a wide range of code
rates can be obtained. We can reach code rates remarkably higher than those
obtainable by the original simplex code, and the price in terms of minimum
distance turns out to be relatively small, leading to interesting trade-offs in
the resulting asymptotic coding gain.
