Design of Rate-Compatible Polar Codes Based on Non-Uniform Channel Polarization

Abstract

In this paper we propose a technique for polar codes (PC) construction for any code length. By default, PC construction is limited to code length proportional to the power of two. To construction the code length arbitrary, puncturing, shortening and extension techniques must be applied. However, performance is degraded with the use of these techniques. Other ways to design polar codes with arbitrary code length but which have encoding and decoding with higher complexity such as multi-kernel, concatenated codes and specific constructions for belief propagation (BP) or successive cancellation list (SCL) decoding. The polarization theory [1] is generalized for non-uniform channels (NUC) and with this approach we can construction rate-compatible PC and variable code length. We developed an implementation algorithm based on the of PC construction by Gaussian approximation (NUPGA). In a scenario where the transmission is over an additive white Gaussian noise (AWGN) channel and under successive cancellation (SC) decoding, the PC construction of arbitrary code length can be implemented with NUPGA. With NUPGA we repolarize the projected synthetic channels by choosing more efficiently the positions of the information bits. In addition, we present a generalization of the Gaussian approximation (GA) for the polarization and repolarization processes and an extension technique for PC. The PC construction based on NUPGA present better performance than the existing techniques as shown in the simulations of this work.

Decoding of Polar Codes Based on Q-Learning-Driven Belief Propagation

“…The BP decoder is a message-passing decoder with iterative processing over the factor graph of any polar code P(N,K) that has found numerous applications in wireless communications [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37]. The factor graph is based on corresponding polarization matrix G ⊗n , composed of n = log 2 N stages, each one with N/2 processing elements (PEs), and (n + 1)N nodes.…”

Study of Polar Codes Based on Piecewise Gaussian Approximation

“…So, the decision g nodes depends on the estimate of f nodes given by (9), that is, of previously decoded bits. Message passing decoding that has found numerous applications in wireless communications [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [32], [31], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48] can also be considered.…”

“…The proposed PGA design of polar codes is presented in its integral form as well as an alternative approximation that does not rely on the integral form. The PGA design can have an impact on the design of rate-compatible polar codes [16], [17], [18], [19]; which are techniques that use GA in their construction. Simulations results show that the proposed PGA design outperforms the standard GA for several examples of polar codes and rates.…”

Polar Codes Based on Piecewise Gaussian Approximation: Design and Analysis

“…Moreover, we show that the difference in accuracy between the approximation methods can be obtained by the Number of Different Positions (NDP), initially introduced by Kern [32], and we derive an index that measures the general quality of the proposed approximation, called Accumulative Design Error (ADE). The rate-compatible PC design that uses GA in its construction, as reported in [33], [34], [35], [36], can have a significant impact on its performance when considered with the APGA and EPGA constructions.…”