Rateless Code Construction On The Real Number Field

Because wireless channel conditions vary with time, it is difficult to achieve high communication rates over wireless networks. To achieve a high throughput, a communication protocol must not only operate at a high rate on a constant channel condition, but also adapt well to variations in noise, attenuation, interference, multipath fading and so on. Current wireless networks solve this problem by providing a large number of physical layer(PHY) configurations or adapting the rate at the transmitter. An alternative approach is to use a rateless code between the transmitter and receiver. An ideal rateless code has the property that communication can occur at a rate close to the channel capacity, but without the sender having to estimate the channel quality and adapt the bit rate explicitly.Besides, most of channel codes used are constructed in the Galois field. It is necessary to convert codewords from Galois field to real number field by modulation for AWGN. For high spectral efficiency, codewords should combine with high-order modulation. But the decoding complexity will increase with the increase of M. Coded modulation can achieve coding gain without the expense of bandwidth expansion. Our proposed rateless encoding scheme is essentially a coded modulation. The main work is summarized as follows:First, we give a brief introduction of the history of traditional error correcting codes and modulation schemes, and then the principle of LT codes. For LT codes, we study the degree distribution and the LT process. Then we discuss the reason of the error floor performance of LT codes over the additive white Gaussian noise channel.Second, we present a novel rateless code constructed on real number field. The sender generates multilevel symbols from binary source through weighted sum operations, and the receiver decodes through belief propagation as LDPC's decoding. Since random projection(RP) symbols are generated by arithmetic addition rather than logical XOR, the belief computation at constraint nodes is much more complex than that in LDPC decoding. We propose two decoding algorithms based on the MAP principle and the elementary signal estimator(ESE) based on Gaussian Approximation(GA). The complexities of the two algorithms are different, but their performances are very close. Then we give the simulation curves to demonstrate the points proposed. Firstly, the bit error rate performance curve of rateless code on the real number field obtained by MAP decoding algorithm and ESE decoding algorithm is given.Then, the bit error rate performance of the rateless code on the real number field with different rates obtained by ESE algorithm based on Gauss approximation is given.Finally, signal-to-noise ratio(SNR) evolution technique is used to evaluate the performance of the GA detector which can provide insight into the convergence properties of iterative decoding. We also figure out the updating rules at constraint nodes and variable nodes.