A sequence-based approximate MMSE decoder for source coding over noisy channels using discrete hidden Markov models

In previous work on source coding over noisy channels it was recognized that when the source has memory, there is typically "residual redundancy" between the discrete symbols produced by the encoder, which can be capitalized upon by the decoder to improve the overall quantizer performance. Sayood and Borkenhagen (1991) and Phamdo and Farvardin (see IEEE Trans. Inform. Theory, vol.40, p.186-93, 1994) proposed "detectors" at the decoder which optimize suitable criteria in order to estimate the sequence of transmitted symbols. Phamdo and Farvardin also proposed an instantaneous approximate minimum mean-squared error (IAMMSE) decoder. These methods provide a performance advantage over conventional systems, but the maximum a posteriori (MAP) structure is suboptimal, while the IAMMSE decoder makes limited use of the redundancy. Alternatively, combining aspects of both approaches, we propose a sequence-based approximate MMSE (SAMMSE) decoder. For a Markovian sequence of encoder-produced symbols and a discrete memoryless channel, we approximate the expected distortion at the decoder under the constraint of fixed decoder complexity. For this simplified cost, the optimal decoder computes expected values based on a discrete hidden Markov model, using the wellknown forward/backward (F/B) algorithm. Performance gains for this scheme are demonstrated over previous techniques in quantizing Gauss-Markov sources over a range of noisy channel conditions. Moreover, a constrained delay version is also suggested.