Polar codes with dynamic frozen symbols and their decoding by directed search

Abstract

A novel construction of polar codes with dynamic frozen symbols is proposed. The proposed codes are subcodes of extended BCH codes, which ensure sufficiently high minimum distance. Furthermore, a decoding algorithm is proposed, which employs estimates of the not-yetprocessed bit channel error probabilities to perform directed search in code tree, reducing thus the total number of iterations.

Design of Polar Codes in 5G New Radio

“…In general, it has been proven that the minimum distance of polar codes can be dramaticaly improved by adding an outer code [41], and SCL decoders can fully exploit this improved code spectrum [42]. Parity-checks (PC) have emerged as an alternative to CRC due to their simplicity and flexibility [41], [43]. Introducing PC bits in the middle of the decoding instead of a single CRC check at the end makes it easier to tune the polar code spectrum; bit-channels corresponding to minimum weight rows are the best candidates to host parity checks [44].…”

Successive cancellation permutation decoding of Reed-Solomon codes

“…It is possible to generalize the construction of polar codes by setting frozen symbols not statically to zero, but to some linear combinations of other symbols (dynamic frozen symbols) [5]. Given any linear code of length n = 2 m with check matrix H, one can represent it as a polar code with dynamic frozen symbols, where the dynamic freezing constraints are given by…”

“…The proposed method exploits representation of Reed-Solomon codes as polar codes [4] with dynamic frozen symbols [5]. This enables application of efficient sequential soft-decision decoding techniques developed in the area of polar coding [6].…”

Optimizing Polar Codes Compatible with Off-the-Shelf LDPC Decoders

“…This concatenation leads to significant performance gains over state-of-the-art low-density parity-check (LDPC) and turbo codes. The concatenation of a polar code with a high-rate parity-check code was likewise introduced in [5] and [6] and shown to be of similar errorrate performance as of the CRC-aided polar codes, with more simplicity and flexibility. The resultant codes enjoy better weight spectrum properties [7] which is regarded as one reason for the improved performance.…”