Optimized Puncturing for the Spinal Codes

As a type of newly invented rateless codes, Spinal codes can achieve the capacity of both additive white Gaussian noise (AWGN) channel and binary symmetric channel (BSC) with short message length and pseudo-random like codewords. In this paper, a novel puncturing pattern called inverted triangle-shaped puncturing is proposed for Spinal codes. We prove a lemma as theoretical support for the proposed inverted triangle-shaped puncturing. Compared with the uniform puncturing pattern, Spinal codes can be punctured to achieve both high and finer-grained rates by the inverted triangle-shaped puncturing, without increasing the cost of decoding. Extensive simulations are carried out to verify the effectiveness of the proposed pattern. Results show that the inverted triangle-shaped puncturing pattern can increase the code rate significantly without any harming to the bit error rate (BER) performance.