Design And Analysis Of Concatenated Spinal Code

Spinal codes are the first category of rateless codes that can be proved to achieve the channel capacity.Spinal codes can generate large amount of pseudo-random bits in rateless transmission by employing hash function sequentially.When channel condition is complex,rateless spinal code can still transmit the information sequence correctly through the continuous transmission of symbols.Although the coding structure of rateless spinal code is very simple and can provide an excellent rate performance,there still has several problems for spinal codes.For example,the sequential encoding structure limits the error performance of spinal code and the tail bits in the information sequence has larger error probability.The decoding complexity of spinal code is relative high in rateless transmission.This dissertation is on the design and analysis of concatenated spinal code,which can provide better error-control performance.The main work of this dissertation includes the following aspects:To overcome the disadvantage of rateless spinal code,especially the poor error-control performance and the high error probability of tail bits,a concatenated spinal coding structure is proposed.By employing an outer code to encode part of the information bits,errors that locate in the tail of the information sequence can be corrected and can improve the errorcontrol performance of rateless spinal code.Based on this concatenated coding strategy,a union decoding algorithm is also designed.Compared to the traditional concatenated decoder,the proposed algorithm decreases part of the computation complexity and improve the performance by employing parity-check and maximum zero span to correct burst errors.In addition,the design of outer code is discussed.By designing the maximum zero span of circulant parity matrix,a series of outer codes can be provided to correct the errors that locate in the tail of the information sequence.Simulation results show that concatenated spinal code can achieve a high transmission rate and good error-control performance.Performance analysis is presented for the concatenated spinal code,including finite-length performance analysis and asymptotic performance analysis.For the finite-length analysis,upper bound on the error probability is derived for concatenated spinal code based on the potential pairwise independent property.Simulation result shows the efficiency of the derived upper bounds,which implies that the derived upper bounds can evaluate the error performance concatenated spinal code.It is shown from the asymptotic analysis that the transmission rate of the concatenated spinal code can be arbitrarily close to the capacity.Then,by employing the sliding window method,this dissertation proves that the capacities of both additive white Gaussian noise channel(AWGN)and binary symmetric channel(BSC)can be achieved by the concatenated spinal code with a union decoder.