Design and Analysis of LT Codes with a Reverse Coding Framework

In this paper, an improved LT code with a reverse coding framework is designed to reduce the error floor caused by low-degree information nodes. For the proposed coding scheme, a well-designed threshold is used to mark the information nodes whose degrees are less than the threshold, and these nodes will be coded reversely to connect to enough candidate check nodes. To design the optimal threshold, firstly, the information degree distribution and the check degree distribution of the improved LT code are deduced. Then, the parameter extrinsic information gain-loss-ratio (GLR) is designed to evaluate the convergence behavior of the improved LT code. Finally, the ‘slow increase region’ of the GLR is set, and the boundary value of this region is used to deduce the optimal threshold which matches with the channel state information (CSI) and decoding overhead. To make the proposed LT code not limited to a fixed code rate, we further modify the proposed scheme. The segment coding method is used to generate a redundant generator matrix, and the check nodes corresponding to this matrix can be transmitted independently and are not limited to a fixed number. Furthermore, the connection relationship between information nodes and check nodes can be easily recorded, which improves the decoding efficiency. The advantages of the improved LT code are that the degree distributions can be formulated, the convergence behavior can be predicted, and the lowest information degree can be adjusted. Simulation results show that the improved LT code can reduce the error floor by up to 4 orders of magnitude. Besides, the designed LT code outperforms the existing LT codes in literature in terms of bit error rate (BER) performance.