Polar Coding Schemes for Cooperative Transmission Systems

: In this thesis, a serially-concatenated coding scheme with a polar code as the outer code and a low density generator matrix (LDGM) code as the inner code is firstly proposed. It is shown that that the proposed scheme provides a method to improve significantly the low convergence of polar codes and the high error floor of LDGM codes while keeping the advantages of both such as the low encoding and decoding complexity. The bit error rate results show that the proposed scheme by reasonable design have the potential to approach a performance close to the capacity limit and avoid error floor effectively. Secondly, a novel transmission protocol based on polar coding is proposed for the degraded half-duplex relay channel. In the proposed protocol, the relay only needs to forward a part of the decoded source message that the destination needs according to the exquisite nested structure of polar codes. It is proved that the scheme can achieve the capacity of the half-duplex relay channel while enjoying low encoding/decoding complexity. By modeling the practical system, we verify that the proposed scheme outperforms the conventional scheme designed by low-density parity-check codes by simulations. Finally, a generalized partial information relaying protocol is proposed for degraded multiple-relay networks with orthogonal receiver components (MRN-ORCs). In such a protocol, each relay node decodes the received source message with the help of partial information from previous nodes and re-encodes part of the decoded message for transmission to satisfy the decoding requirements for the following relay node or the destination node. For the design of polar codes, the nested structures are constructed based on this protocol and the information sets corresponding to the partial messages forwarded are also calculated. It is proved that the proposed scheme achieves the theoretical capacity of the degraded MRN-ORCs while still retains the low-complexity feature of polar codes

The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure

Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed by exploiting a concatenated code structure, which invokes iterative decoding. Therefore, in this paper we provide an extensive step-by-step tutorial for designing EXtrinsic Information Transfer (EXIT) chart aided concatenated quantum codes based on the underlying quantum-to-classical isomorphism. These design lessons are then exemplified in the context of our proposed Quantum Irregular Convolutional Code (QIRCC), which constitutes the outer component of a concatenated quantum code. The proposed QIRCC can be dynamically adapted to match any given inner code using EXIT charts, hence achieving a performance close to the hashing bound. It is demonstrated that our QIRCC-based optimized design is capable of operating within 0.4 dB of the noise limit

Polar Code: An Advanced Encoding And Decoding Architecture For Next Generation 5G Applications

Polar Codes become a new channel coding, which will be common to apply for next-generation wireless communication systems. Polar codes, introduced by Arikan, achieves the capacity of symmetric channels with “low encoding and decoding complexity” for a large class of underlying channels. Recently, polar code has become the most favorable error correcting code in the viewpoint of information theory due to its property of channel achieving capacity. Polar code achieves the capacity of the class of symmetric binary memory less channels. In this paper review of polar code, an advanced encoding and decoding architecture for next generation applications

Polar Coding for the Large Hadron Collider: Challenges in Code Concatenation

In this work, we present a concatenated repetition-polar coding scheme that is aimed at applications requiring highly unbalanced unequal bit-error protection, such as the Beam Interlock System of the Large Hadron Collider at CERN. Even though this concatenation scheme is simple, it reveals significant challenges that may be encountered when designing a concatenated scheme that uses a polar code as an inner code, such as error correlation and unusual decision log-likelihood ratio distributions. We explain and analyze these challenges and we propose two ways to overcome them.Comment: Presented at the 51st Asilomar Conference on Signals, Systems, and Computers, November 201