BER bounds on parallel concatenated single parity check arrays and zigzag codes

A union bound analysis of the bit error probability of parallel concatenated single parity check (SPC) array and zigzag code is presented. It is shown that the union bounds for these codes can be generated very efficiently. It is also shown that the simple codes studied can achieve comparable performances as the turbo codes (yet has much lower decoding costs as discussed in an earlier paper). It illustrates that, for a fixed interleaver size, the concatenated code has increased code potential as its dimension, i.e., the number of interleavers, increases (which raises decoding costs linearly, not exponentially as for increased constraint length). Finally, the analysis shows that the zigzag codes with dimension greater than three have lower error floors than comparable two-dimensional turbo codes.