Is feedback a performance equalizer of classic and modern codes?

It is well known that in general, feedback cannot increase the capacity of a discrete memoryless channel. However, it can help simplify the complexity of encoding and decoding. Schalkwijk and Kailath (1966) developed a class of block codes for Gaussian channels with ideal feedback. They showed that the probability of decoding error decreases as a second-order exponent in block length for rates below capacity. This paper proposes a coding scheme with ideal feedback and is applied to punctured convolutional codes and punctured Turbo codes. Our results seem to indicate that feedback largely equalizes the performance of classic (convolutional) codes and modern (turbo, LDPC) codes.