Performance Analysis Of Finite-Length Spatially Coupled RA Codes

Spatially coupled RA codes is a new class of spatially coupled codes, based on regular RA codes. Compared to spatially coupled LDPC codes with same thresholds and decoding complexity, spatially coupled RA codes have simpler encoders and slightly higher code rates. In addition, the threshold saturation will still appears. the belief propagation thresholds of spatially coupled RA codes are closed to the maximum-a-posteriori (MAP) thresholds of the regular RA codes.In this thesis, we first analysis the number of decoding iteration of spatially coupled RA codes. From the simulation results, we can see that the needed iteration number scales linearly in L. The larger L, the more iterations we need to achieve the same correct decoding probability. The simulation results show that, at the certain coupled length L, to achieve a certain value of correct decoding probability, the number of iterations needed for spatially coupled RA codes with large M will close to an average value.Secondly, we study the scaling behavior of spatially coupled RA codes base on scaling function, L=f(M). When L is fixed, the simulation results indicate that with the increase of M, the bit error probability curves become steeper, which means the behavior becomes better, as well as the error floor becomes lower. When M is fixed, we can observe from the simulation results that with the increasing of L, the error probability is monotonically increasing in L. This is because that the longer the chain, the higher the chance that the "decoding wave" gets stuck. According to the simulation results, we can find that the curves will converge to a limiting curve. When L is a general function of M, we mainly study the functions L= M and L=(M/2)2. For these scaling functions, the simulation results the bit error probability of spatially coupled RA codes decrease with increasing M, and the behavior becomes better. Then, we conclude that for most scaling functions L=f(M), the threshold situation of spatially coupled RA codes will be appearing. Hence, the threshold saturation is robust and general.Finally, we introduce the PD decoding algorithm, and deduce the expected graph evolution and covariance evolution of spatially coupled RA codes. This is the preparation work of predicting the behavior of spatiallv coupled RA codes in waterfall region.