Primitive Rateless Codes

In this paper, we propose primitive rateless (PR) codes. A PR code is characterized by the message length and a polynomial over $\mathbf{GF}(2)$, which can generate potentially limitless number of coded symbols. We show that codewords truncated at any arbitrary be represented as subsequences maximum-length sequence ($m$-sequence). characterize Hamming weight distribution codes their duals for properly chosen polynomial, well approximated binomial distribution. further find lower bound on minimum there always exists meet desired codeword length. provide list polynomials lengths up to $40$ respective closely Gilbert-Varshamov various rates. Simulation results achieve similar block error rates BCH counterparts signal-to-noise ratios (SNRs) are rate-compatible many symbols required; thus, demonstrating truly performance.