Design of optimised multiple partial recovery LT codes

Abstract

Existing rateless codes have a very low intermediate symbol recovery rate. Therefore, a new analysis method named iterative and small degree first (I-SDF) is presented for the design of optimised partial recovery Luby transform codes (PR-LTC) in this study. On the basis of I-SDF, the required number of encoded symbols with degree d in each decoding step is calculated by an iterative optimisation algorithm. Under the proposed design, R(R < k) input symbols can be recovered from as few encoded symbols as possible in PR-LTC with message length k. Furthermore, multiple PR-LTC (M-PR-LTC) is proposed to recover several partial recovery point (PRPs) efficiently. The analysis process is divided into multiple stages, and the required number of encoded symbols with degree d in each decoding step is calculated by a cross-stage iterative optimisation algorithm. In addition, the interaction of each stage is adjusted by introducing a weight for each PRP. The PR-LTC and M-PR-LTC are evaluated and compared with the existing schemes. The simulation results demonstrate that PR-LTC and M-PR-LTC outperform other existing schemes in terms of average overhead, average degree of encoded symbols, memory usage, bit error rate and energy consumption.