Accumulating LDPC (Low Density Parity Check) decoder. The accumulating decoding architecture described herein is applicable to LDPC codes operating on a parity check matrix, H, consisting of CSI (Cyclic Shifted Identity) sub-matrices (or matrix sub-blocks) or permuted identity sub-matrices (or matrix sub-blocks). In such a structure, the entire LDPC matrix is broken into square sub-matrices such that each sub-matrix consists of either a CSI sub-matrix or a permuted identity sub-matrix, or a null matrix. The iterative decoding process operates by updating of APP (a posteriori probability) or gamma (γ) values and check edge message (λ) values, and this by updating one or more individual rows within a number of sub-matrix rows (or all sub-matrix or sub-block rows) are processed in parallel. The amount of parallelism is specified by the designer and is typically an integer divisor of the sub-matrix (or sub-block) size.