A Controllable Complexity Soft-Output Suboptimal Convolutional Decoder

Suboptimal decoding of convolutional codes, motivated by the need to deal with large constraint length codes, has in the past been achieved by stack algorithms or sequential decoding, which typically do not produce soft outputs, which may be desirable in some modern iterative decoding frame-works. Motivated by an approximate posterior equalizer, we present a suboptimal decoder which employs a similar decomposition for binary convolutional codes observed in additive white Gaussian noise. This results in mixed-field arithmetic (GF(2) and R). The GF(2) (convolutional code) arithmetic means that the central limit theorem does not apply. Instead, we invoke Gallager´s lemma to compute the distribution of the interfering terms. Under various assumptions of independence (resulting in different complexities) the channel posterior probability can be approximated, resulting in a soft-output decoder. Initial results indicate effective performance when dependencies among rows are incorporated. The method may also extend to arbitrary binary linear codes.