Concatenated codes: serial and parallel
An analogy is examined between serially concatenated codes and parallel concatenations whose interleavers are described by bipartite graphs with good expanding properties. In particular, a modified expander code construction is shown to behave very much like Forney's classical concatenated codes, though with improved decoding complexity. It is proved that these new codes achieve the Zyablov bound δZ on the minimum distance. For these codes, a soft-decision, reliability-based, linear-time decoding algorithm is introduced, that corrects any fraction of errors up to almost δZ/2. For the binary-symmetric channel, this algorithm's error exponent attains the Forney bound previously known only for classical (serial) concatenations.