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This paper reconsiders the iterative soft decision feedback zigzag algorithm (ISDFZA) of Chen et. al. (IEEE JSAC, Feb. 2010), for equalization of two-dimensional intersymbol interference channels with additive white Gaussian noise. In the ISDFZA, source pixel estimates were assumed to be statistically independent; in the new algorithm we jointly estimate adjacent groups of source pixels. The new algorithm, called the block zigzag (BLKZ) algorithm, uses constant LLR weights across iterations, and provides more than 2 dB SNR gain over the ISDFZA on the 2×2 averaging mask channel; at low and medium SNRs it also outperforms the iterative row-column soft decision feedback algorithm (IRCSDFA) using joint extrinsic information (Chen et. al., CISS 2010). For the 3 × 3 averaging mask, the BLKZ algorithm gives more than 1 dB SNR gain over the independent ISDFZA at high SNRs. When the BLKZ algorithm is concatenated with the joint IRCSDFA, the concatenated system achieves the maximum-likelihood (ML) bound at high SNR with the 2 × 2 averaging mask; with the 3 × 3 averaging mask the joint concatenated system gains about 1 dB compared to the concatenated system with independence assumption, and comes within 0.2 dB of the ML bound. This paper also introduces a new method of LLR subtraction for the BLKZ algorithm based on the algorithms two-dimensional extrinsic information flow chart.