Iterative channel equalization, channel decoding and source decoding

The performance of soft source decoding is evaluated over dispersive AWGN channels. By employing source codes having error-correcting capabilities, such as Reversible Variable-Length Codes (RVLCs) and Variable-Length Error-Correcting (VLEC) codes, the softin/soft-out (SISO) source decoder benefits from exchanging information with the MAP equalizer, and effectively eliminates the inter-symbol interference (ISI) after a few iterations. It was also found that the soft source decoder is capable of significantly improving the attainable performance of the turbo receiver provided that channel equalization, channel decoding and source decoding are carried out jointly and iteratively. At SER = 10-4, the performance of this three-component turbo receiver is about 2 dB better in comparison to the benchmark scheme carrying out channel equalization and channel decoding jointly, but source decoding separately. At this SER value, the performance of the proposed scheme is about 1 dB worse than that of the ½-rate convolutional coded non-dispersive AWGN channel.<br/

Turbo Detection of Space-time Trellis-Coded Constant Bit Rate Vector-Quantised Videophone System using Reversible Variable-Length Codes, Convolutional Codes and Turbo Codes

In this treatise we characterise the achievable performance of a proprietary video transmission system, which employs a Constant Bit Rate (CBR) video codec that is concatenated with one of three error correction codecs, namely a Reversible Variable-Length Code (RVLC), a Convolutional Code (CC) or a convolutional-based Turbo Code (TC). In our investigations, the CBR video codec was invoked in conjunction with Space-Time Trellis Coding (STTC) designed for transmission over a dispersive Rayleigh fading channel. At the receiver, the channel equaliser, the STTC decoder and the RVLC, CC or TC decoder, as appropriate, employ the Max-Log Maximum A-Posteriori (MAP) algorithm and their operations are performed in an iterative 'turbo-detection' fashion. The systems were designed for maintaining similar error-free video reconstruction qualities, which were found to be subjectively pleasing at a Peak Signal to Noise Ratio (PSNR) of 30.6~dB, at a similar decoding complexity per decoding iteration. These design criteria were achieved by employing differing transmission rates, with the CC- and TC-based systems having a 22% higher bandwidth requirement. The results demonstrated that the TC-, RVLC- and CC-based systems achieve acceptable subjective reconstructed video quality associated with an average PSNR in excess of 30~dB for $E_b/N_0$ values above 4.6~dB, 6.4~dB and 7.7~dB, respectively. The design choice between the TC- and RVLC-based systems constitutes a trade-off between the increased error resilience of the TC-based scheme and the reduced bandwidth requirement of the RVLC-based scheme

A MILP approach for designing robust variable-length codes based on exact free distance computation

International audienceThis paper addresses the design of joint source-channel variable-length codes with maximal free distance for given codeword lengths. While previous design methods are mainly based on bounds on the free distance of the code, the proposed algorithm exploits an exact characterization of the free distance. The code optimization is cast in the framework of mixed-integer linear programming and allows to tackle practical alphabet sizes in reasonable computing time

On privacy amplification, lossy compression, and their duality to channel coding

We examine the task of privacy amplification from information-theoretic and coding-theoretic points of view. In the former, we give a one-shot characterization of the optimal rate of privacy amplification against classical adversaries in terms of the optimal type-II error in asymmetric hypothesis testing. This formulation can be easily computed to give finite-blocklength bounds and turns out to be equivalent to smooth min-entropy bounds by Renner and Wolf [Asiacrypt 2005] and Watanabe and Hayashi [ISIT 2013], as well as a bound in terms of the $E_\gamma$ divergence by Yang, Schaefer, and Poor [arXiv:1706.03866 [cs.IT]]. In the latter, we show that protocols for privacy amplification based on linear codes can be easily repurposed for channel simulation. Combined with known relations between channel simulation and lossy source coding, this implies that privacy amplification can be understood as a basic primitive for both channel simulation and lossy compression. Applied to symmetric channels or lossy compression settings, our construction leads to proto- cols of optimal rate in the asymptotic i.i.d. limit. Finally, appealing to the notion of channel duality recently detailed by us in [IEEE Trans. Info. Theory 64, 577 (2018)], we show that linear error-correcting codes for symmetric channels with quantum output can be transformed into linear lossy source coding schemes for classical variables arising from the dual channel. This explains a "curious duality" in these problems for the (self-dual) erasure channel observed by Martinian and Yedidia [Allerton 2003; arXiv:cs/0408008] and partly anticipates recent results on optimal lossy compression by polar and low-density generator matrix codes.Comment: v3: updated to include equivalence of the converse bound with smooth entropy formulations. v2: updated to include comparison with the one-shot bounds of arXiv:1706.03866. v1: 11 pages, 4 figure

New Free Distance Bounds and Design Techniques for Joint Source-Channel Variable-Length Codes

International audienceThis paper proposes branch-and-prune algorithms for searching prefix-free joint source-channel codebooks with maximal free distance for given codeword lengths. For that purpose, it introduces improved techniques to bound the free distance of variable-length codes

Functional diagnosability and recovery from massive faults in digital systems Quarterly progress reports, 17 May - 16 Nov. 1970 /final/

Diagnosability and recovery from massive faults in digital system

Polynomial-time T-depth Optimization of Clifford+T circuits via Matroid Partitioning

Most work in quantum circuit optimization has been performed in isolation from the results of quantum fault-tolerance. Here we present a polynomial-time algorithm for optimizing quantum circuits that takes the actual implementation of fault-tolerant logical gates into consideration. Our algorithm re-synthesizes quantum circuits composed of Clifford group and T gates, the latter being typically the most costly gate in fault-tolerant models, e.g., those based on the Steane or surface codes, with the purpose of minimizing both T-count and T-depth. A major feature of the algorithm is the ability to re-synthesize circuits with additional ancillae to reduce T-depth at effectively no cost. The tested benchmarks show up to 65.7% reduction in T-count and up to 87.6% reduction in T-depth without ancillae, or 99.7% reduction in T-depth using ancillae.Comment: Version 2 contains substantial improvements and extensions to the previous version. We describe a new, more robust algorithm and achieve significantly improved experimental result