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Gradient Projection Decoding of LDPC Codes

A new practical method for decoding low-density parity check (LDPC) codes is presented. The followed approach involves reformulating the parity check equations using nonlinear functions of a specific form, defined over Rrho, where rho denotes the check node degree. By constraining the inputs to these functions in the closed convex subset [0,1]rho ("box" set) of Rrho, and also by exploiting their form, a multimodal objective function that entails the code constraints is formulated. The gradient projection algorithm is then used for searching for a valid codeword that lies in the vicinity of the channel observation. The computational complexity of the new decoding technique is practically sub-linearly dependent on the code's length, while processing on each variable node can be performed in parallel allowing very low decoding latencies. Simulation results show that convergence is achieved within 10 iterations, although some performance degradations relative to the belief propagation (BP) algorithm are observed