In this paper we introduce a reconstruction approach for the input signal of an oversampled filter bank (OFB) when the subbands generated at its output are quantized and transmitted over a noisy channel. We exploit the redundancy introduced by the OFB and the bounded quantization noise in order to construct a consistent estimator that corrects transmission errors. A maximum-likelihood estimation of the quantization indexes transmitted over the channel is evaluated, which only considers the vectors of quantization indexes corresponding to subband signals that could have been generated by the OFB and that are compliant with the quantization errors. Neither hypothesis tests nor specific parameters need to be set or computed in advance as is the case in approaches presented in \cite{Redinbo00,LabeauChiang2004}. When considering an OFB with oversampling ratio $3/2$, a BPSK modulation of the quantized subbands and a transmission over an AWGN channel, compared to a classical decoder, the gain is about $8$ dB in terms of reconstructed signal SNR for a channel SNR of $7$ dB.