Side-Information Coding with Turbo Codes and its Application to Quantum Key Distribution

Turbo coding is a powerful class of forward error correcting codes, which can achieve performances close to the Shannon limit. The turbo principle can be applied to the problem of side-information source coding, and we investigate here its application to the reconciliation problem occurring in a continuous-variable quantum key distribution protocol.Comment: 3 pages, submitted to ISITA 200

Turbo Decoding and Detection for Wireless Applications

A historical perspective of turbo coding and turbo transceivers inspired by the generic turbo principles is provided, as it evolved from Shannon’s visionary predictions. More specifically, we commence by discussing the turbo principles, which have been shown to be capable of performing close to Shannon’s capacity limit. We continue by reviewing the classic maximum a posteriori probability decoder. These discussions are followed by studying the effect of a range of system parameters in a systematic fashion, in order to gauge their performance ramifications. In the second part of this treatise, we focus our attention on the family of iterative receivers designed for wireless communication systems, which were partly inspired by the invention of turbo codes. More specifically, the family of iteratively detected joint coding and modulation schemes, turbo equalization, concatenated spacetime and channel coding arrangements, as well as multi-user detection and three-stage multimedia systems are highlighted

Turbo codes and turbo algorithms

In the first part of this paper, several basic ideas that prompted the coming of turbo codes are commented on. We then present some personal points of view on the main advances obtained in past years on turbo coding and decoding such as the circular trellis termination of recursive systematic convolutional codes and double-binary turbo codes associated with Max-Log-MAP decoding. A novel evaluation method, called genieinitialised iterative processing (GIIP), is introduced to assess the error performance of iterative processing. We show that using GIIP produces a result that can be viewed as a lower bound of the maximum likelihood iterative decoding and detection performance. Finally, two wireless communication systems are presented to illustrate recent applications of the turbo principle, the first one being multiple-input/multiple-output channel iterative detection and the second one multi-carrier modulation with linear precoding

The Error-Pattern-Correcting Turbo Equalizer

The error-pattern correcting code (EPCC) is incorporated in the design of a turbo equalizer (TE) with aim to correct dominant error events of the inter-symbol interference (ISI) channel at the output of its matching Viterbi detector. By targeting the low Hamming-weight interleaved errors of the outer convolutional code, which are responsible for low Euclidean-weight errors in the Viterbi trellis, the turbo equalizer with an error-pattern correcting code (TE-EPCC) exhibits a much lower bit-error rate (BER) floor compared to the conventional non-precoded TE, especially for high rate applications. A maximum-likelihood upper bound is developed on the BER floor of the TE-EPCC for a generalized two-tap ISI channel, in order to study TE-EPCC's signal-to-noise ratio (SNR) gain for various channel conditions and design parameters. In addition, the SNR gain of the TE-EPCC relative to an existing precoded TE is compared to demonstrate the present TE's superiority for short interleaver lengths and high coding rates.Comment: This work has been submitted to the special issue of the IEEE Transactions on Information Theory titled: "Facets of Coding Theory: from Algorithms to Networks". This work was supported in part by the NSF Theoretical Foundation Grant 0728676