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

Deriving Good LDPC Convolutional Codes from LDPC Block Codes

Low-density parity-check (LDPC) convolutional codes are capable of achieving excellent performance with low encoding and decoding complexity. In this paper we discuss several graph-cover-based methods for deriving families of time-invariant and time-varying LDPC convolutional codes from LDPC block codes and show how earlier proposed LDPC convolutional code constructions can be presented within this framework. Some of the constructed convolutional codes significantly outperform the underlying LDPC block codes. We investigate some possible reasons for this "convolutional gain," and we also discuss the --- mostly moderate --- decoder cost increase that is incurred by going from LDPC block to LDPC convolutional codes.Comment: Submitted to IEEE Transactions on Information Theory, April 2010; revised August 2010, revised November 2010 (essentially final version). (Besides many small changes, the first and second revised versions contain corrected entries in Tables I and II.

Short Block-length Codes for Ultra-Reliable Low-Latency Communications

This paper reviews the state of the art channel coding techniques for ultra-reliable low latency communication (URLLC). The stringent requirements of URLLC services, such as ultra-high reliability and low latency, have made it the most challenging feature of the fifth generation (5G) mobile systems. The problem is even more challenging for the services beyond the 5G promise, such as tele-surgery and factory automation, which require latencies less than 1ms and failure rate as low as $10^{-9}$. The very low latency requirements of URLLC do not allow traditional approaches such as re-transmission to be used to increase the reliability. On the other hand, to guarantee the delay requirements, the block length needs to be small, so conventional channel codes, originally designed and optimised for moderate-to-long block-lengths, show notable deficiencies for short blocks. This paper provides an overview on channel coding techniques for short block lengths and compares them in terms of performance and complexity. Several important research directions are identified and discussed in more detail with several possible solutions.Comment: Accepted for publication in IEEE Communications Magazin

Concatenated Turbo/LDPC codes for deep space communications: performance and implementation

Deep space communications require error correction codes able to reach extremely low bit-error-rates, possibly with a steep waterfall region and without error floor. Several schemes have been proposed in the literature to achieve these goals. Most of them rely on the concatenation of different codes that leads to high hardware implementation complexity and poor resource sharing. This work proposes a scheme based on the concatenation of non-custom LDPC and turbo codes that achieves excellent error correction performance. Moreover, since both LDPC and turbo codes can be decoded with the BCJR algorithm, our preliminary results show that an efficient hardware architecture with high resource reuse can be designe

Advanced channel coding for space mission telecommand links

We investigate and compare different options for updating the error correcting code currently used in space mission telecommand links. Taking as a reference the solutions recently emerged as the most promising ones, based on Low-Density Parity-Check codes, we explore the behavior of alternative schemes, based on parallel concatenated turbo codes and soft-decision decoded BCH codes. Our analysis shows that these further options can offer similar or even better performance.Comment: 5 pages, 7 figures, presented at IEEE VTC 2013 Fall, Las Vegas, USA, Sep. 2013 Proc. IEEE Vehicular Technology Conference (VTC 2013 Fall), ISBN 978-1-6185-9, Las Vegas, USA, Sep. 201