Joint source/channel decoders that use the residual redundancy in the source are investigated for differential pulse code modulation (DPCM) picture transmission over a binary symmetric channel. Markov sequence decoders employing the Viterbi algorithm that use first-order source statistics are reviewed, and generalized for decoders that use second-order source statistics. To make optimal use of the source correlation in both horizontal and vertical directions, it is necessary to generalize the conventional Viterbi decoding algorithm for a one higher-dimensional trellis. The paths through the trellis become two-dimensional "sheets", thus, the technique is coined "sheet decoding". By objective [reconstruction signal-to-noise ratio (SNR)] and subjective measure, it is found that the sheet decoders outperform the Markov sequence decoders that use a first-order Markov model, and outperform two other known decoders (modified maximum a posteriori probability and maximal SNR) that use a second-order Markov model. Moreover, it is found that the use of a simple rate-2/3 block code in conjunction with Markov model-aided decoding (MMAD) offers significant performance improvement for a 2-bit DPCM system. For the example Lenna image, it is observed that the rate-2/3 block code is superior to a rate-2/3 convolutional code for channel-error rates higher than 0.035. The block code is easily incorporated into any of the MMAD DPCM systems and results in a 2-bit MMAD DPCM system that significantly outperforms the noncoded 3-bit MMAD DPCM systems for channel-error rates higher than 0.04.

Soft-decision-feedback MAP decoders are developed for joint source/channel decoding (JSCD) which uses the residual redundancy in two-dimensional sources. The source redundancy is described by a second order Markov model which is made available to the receiver for row-by-row decoding, wherein the output for one row is used to aid the decoding of the next row. Performance can be improved by generalizing so as to increase the vertical depth of the decoder. This is called sheet decoding, and entails generalizing trellis decoding of one-dimensional data to trellis decoding of two-dimensional data (2-D). The proposed soft-decision-feedback sheet decoder is based on the Bahl algorithm, and it is compared to a hard-decision-feedback sheet decoder which is based on the Viterbi algorithm. The method is applied to 3-bit DPCM picture transmission over a binary symmetric channel, and it is found that the soft-decision-feedback decoder with vertical depth V performs approximately as well as the hard-decision-feedback decoder with vertical depth V+1. Because the computational requirement of the decoders depends exponentially on the vertical depth, the soft-decision-feedbark decoder offers significant reduction in complexity. For standard monochrome Lena, at a channel bit error rate of 0.05, the V=1 and V=2 soft-decision-feedback decoder JSCD gains in RSNR are 5.0 and 6.3 dB, respectively.