Regularized Variable-Node LT Codes with Improved Erasure Floor Performance

We consider the use of extrinsic information transfer charts for the design of Luby Transform (LT) codes over the binary erasure channel (BEC). In particular, we formulate an optimization problem to determine asymptotically good checknode degree distributions in terms of decoder overhead. We further propose a modified encoding scheme that maximizes the minimum variable-node degree, thus optimizing the erasure-floor performance at the expense of decoder overhead, and resulting in a regularized variable-node degree distribution. The two approaches are combined to jointly improve decoder overhead and decoder erasure floor by incorporating the proposed encoding strategy into the convex optimization problem. The performance of the proposed schemes is investigated for transmission over the BEC through density evolution and numerical simulations. The optimized codes compare favorably to conventional LT codes, and are further extended to enable improved performance for unequal erasure protection.