Trellis-constrained Codes

We introduce a class of iteratively decodable trellis-constrained codes as a generalization of turbocodes, low-density parity-check codes, serially-concatenated con-volutional codes, and product codes. In a trellis-constrained code, multiple trellises interact to deene the allowed set of codewords. As a result of these interactions, the minimum-complexity single trellis for the code can have a state space that grows exponentially with block length. However, as with turbocodes and low-density parity-check codes, a decoder can approximate bit-wise maximum a posteriori decoding by using the sum-product algorithm on the factor graph that describes the code. We present two new families of codes, homogenous trellis-constrained codes and ring-connected trellis-constrained codes, and give results that show these codes perform in the same regime as do turbo-codes and low-density parity-check codes.