Abstract: A block-parallel decoding algorithm and corresponding decoder architecture utilizes a set of interconnected processing nodes configured in the form of a probability dependency graph. The probability dependency graph is characterized at least in part by a code used to encode blocks of bits or symbols, and the processing nodes implement a block-parallel decoding process for blocks of the bits or symbols to be decoded. The probability dependency graph may be, for example, a bipartite probability dependency graph which includes a set of N variable nodes and a set of T check nodes, with one of the N variable nodes being associated with each of N bits or symbols of a given block to be decoded. A single iteration of the block-parallel decoding process produces within the variable nodes an updated estimate for every bit or symbol in the given block, and may produce within the variable nodes an a-posteriori probability associated with the decoded bit or symbol for a soft-decision decoder.