RELIABILITY FUNCTIONS FOR CONCATENATED CODES EMPLOYING MODULAR CODES WITH MAXIMUM-LIKELIHOOD DECODING

This paper investigates the error correcting capabilities of concatena ted codes employing algebraic geometry codes as outer codes and time-v arying randomly selected inner codes, used on discrete memoryless chan nels with maximum likelihood decoding. It is proved that Gallager's ra ndom coding error exponent can be obtained for all rates by such codes . Further, it is clarified that the error exponent arbitrarily close t o Gallager's can be obtained for almost all random selections of inner codes with a properly chosen code length, provided that the length of the outer code is sufficiently large. For a class of regular channels , the result is also valid for linear concatenated codes, and Gallager 's expurgated error exponent can be asymptotically obtained for all ra tes.