Analysis and Design of Partially Information- and Partially Parity-Coupled Turbo Codes

In this paper, we study a class of spatially coupled turbo codes, namely partially information- and partially parity-coupled turbo codes. This class of codes enjoy several advantages such as flexible code rate adjustment by varying the coupling ratio and the encoding and decoding architectures of the underlying component codes can remain unchanged. For this work, we first provide the construction methods for partially coupled turbo codes with coupling memory $m$ and study the corresponding graph models. We then derive the density evolution equations for the corresponding ensembles on the binary erasure channel to precisely compute their iterative decoding thresholds. Rate-compatible designs and their decoding thresholds are also provided, where the coupling and puncturing ratios are jointly optimized to achieve the largest decoding threshold for a given target code rate. Our results show that for a wide range of code rates, the proposed codes attain close-to-capacity performance and the decoding performance improves with increasing the coupling memory. In particular, the proposed partially parity-coupled turbo codes have thresholds within 0.0002 of the BEC capacity for rates ranging from $1/3$ to $9/10$, yielding an attractive way for constructing rate-compatible capacity-approaching channel codes.Comment: 15 pages, 13 figures. Accepted for publication in IEEE Transactions on Communication

Partially Coupled Codes for TB-based Transmission

In this thesis, we mainly investigate the design of partially coupled codes for transport block (TB) based transmission protocol adopted in 4G/5G mobile network standards. In this protocol, an information sequence in a TB is segmented into multiple code blocks (CBs) and each CB is protected by a channel codeword independently. It is inefficient in terms of transmit power and spectrum efficiency because any erroneous CB in a TB leads to the retransmission of the whole TB. An important research problem related to this TB-based transmission is how to improve the TB error rate (TBER) performance so that the number of retransmissions reduces. To tackle this challenge, we present a class of spatial coupling techniques called partial coupling in the TB encoding operation, which has two subclasses: partial information coupled (PIC) and partial parity coupling (PPC). To be specific, the coupling is performed such that a fraction of the information/parity sequence of one component code at the current CB is used as the input of the component encoder at the next CB, leading to improved TBER performance. One of the appealing features of partial coupling (both PIC and PPC) is that the coupling can be applied to any component codes without changing their encoding and decoding architectures, making them compatible with the TB-based transmission protocol. The main body of this thesis consists of two parts. In the first part, we apply both PIC and PPC to turbo codes. We investigate various coupling designs and analysis the performance of the partially coupled turbo codes over the binary erasure channel via density evolution (DE). Both simulation results and DE analysis show that such a class of codes can approach channel capacity with a large blocklength. In the second part, we construct PIC-polar codes. We show that PIC can effectively improve the error performance of finite-length polar codes by utilizing the channel polarization phenomenon. The DE-based performance analysis is also conducted. For both turbo codes and polar codes, we have shown that the partially coupled codes have significant performance gain over their uncoupled counterpart, demonstrating the effectiveness of the partial coupling