Partitioned List Decoding of Polar Codes: Analysis and Improvement of Finite Length Performance

TL;DR

This paper analyzes and improves partitioned list decoding of polar codes, enhancing finite length performance through code construction, CRC allocation, and theoretical bounds, with implications for 5G communication systems.

Contribution

It introduces a new code construction, an optimal CRC allocation scheme, and an upper bound on list size for improved PSCL decoding performance.

Findings

Enhanced finite length performance without extra cost

Optimal CRC allocation scheme for PSCL decoding

Upper bound on list size for MAP performance

Abstract

Polar codes represent one of the major recent breakthroughs in coding theory and, because of their attractive features, they have been selected for the incoming 5G standard. As such, a lot of attention has been devoted to the development of decoding algorithms with good error performance and efficient hardware implementation. One of the leading candidates in this regard is represented by successive-cancellation list (SCL) decoding. However, its hardware implementation requires a large amount of memory. Recently, a partitioned SCL (PSCL) decoder has been proposed to significantly reduce the memory consumption. In this paper, we examine the paradigm of PSCL decoding from both theoretical and practical standpoints: (i) by changing the construction of the code, we are able to improve the performance at no additional computational, latency or memory cost, (ii) we present an optimal scheme to allocate cyclic redundancy checks (CRCs), and (iii) we provide an upper bound on the list size that allows MAP performance.