Quantum serial turbo-codes

We present a theory of quantum serial turbo-codes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum LDPC codes. First, the Tanner graph used for decoding is free of 4-cycles that deteriorate the performances of iterative decoding. Secondly, the iterative decoder makes explicit use of the code's degeneracy. Finally, there is complete freedom in the code design in terms of length, rate, memory size, and interleaver choice. We define a quantum analogue of a state diagram that provides an efficient way to verify the properties of a quantum convolutional code, and in particular its recursiveness and the presence of catastrophic error propagation. We prove that all recursive quantum convolutional encoder have catastrophic error propagation. In our constructions, the convolutional codes have thus been chosen to be non-catastrophic and non-recursive. While the resulting families of turbo-codes have bounded minimum distance, from a pragmatic point of view the effective minimum distances of the codes that we have simulated are large enough not to degrade the iterative decoding performance up to reasonable word error rates and block sizes. With well chosen constituent convolutional codes, we observe an important reduction of the word error rate as the code length increases.Comment: 24 pages, 15 figures, Published versio

Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications

Coding; Communications; Engineering; Networks; Information Theory; Algorithm

On the iterative decoding of sparse quantum codes

We address the problem of decoding sparse quantum error correction codes. For Pauli channels, this task can be accomplished by a version of the belief propagation algorithm used for decoding sparse classical codes. Quantum codes pose two new challenges however. Firstly, their Tanner graph unavoidably contain small loops which typically undermines the performance of belief propagation. Secondly, sparse quantum codes are by definition highly degenerate. The standard belief propagation algorithm does not exploit this feature, but rather it is impaired by it. We propose heuristic methods to improve belief propagation decoding, specifically targeted at these two problems. While our results exhibit a clear improvement due to the proposed heuristic methods, they also indicate that the main source of errors in the quantum coding scheme remains in the decoding.Comment: To appear in QI

Preserving data integrity of encoded medical images: the LAR compression framework

International audienceThrough the development of medical imaging systems and their integration into a complete information system, the need for advanced joint coding and network services becomes predominant. PACS (Picture Archiving and Communication System) aims to acquire, store and compress, retrieve, present and distribute medical images. These systems have to be accessible via the Internet or wireless channels. Thus protection processes against transmission errors have to be added to get a powerful joint source-channel coding tool. Moreover, these sensitive data require confidentiality and privacy for both archiving and transmission purposes, leading to use cryptography and data embedding solutions. This chapter introduces data integrity protection and developed dedicated tools of content protection and secure bitstream transmission for medical encoded image purposes. In particular, the LAR image coding method is defined together with advanced securization services

The Telecommunications and Data Acquisition Report

This quarterly publication provides archival reports on developments in programs managed by JPL's Telecommunications and Mission Operations Directorate (TMOD), which now includes the former Telecommunications and Data Acquisition (TDA) Office. In space communications, radio navigation, radio science, and ground-based radio and radar astronomy, it reports on activities of the Deep Space Network (DSN) in planning, supporting research and technology, implementation, and operations. Also included are standards activity at JPL for space data and information systems and reimbursable DSN work performed for other space agencies through NASA. The preceding work is all performed for NASA's Office of Space Communications (OSC)

Near-capacity fixed-rate and rateless channel code constructions

Fixed-rate and rateless channel code constructions are designed for satisfying conflicting design tradeoffs, leading to codes that benefit from practical implementations, whilst offering a good bit error ratio (BER) and block error ratio (BLER) performance. More explicitly, two novel low-density parity-check code (LDPC) constructions are proposed; the first construction constitutes a family of quasi-cyclic protograph LDPC codes, which has a Vandermonde-like parity-check matrix (PCM). The second construction constitutes a specific class of protograph LDPC codes, which are termed as multilevel structured (MLS) LDPC codes. These codes possess a PCM construction that allows the coexistence of both pseudo-randomness as well as a structure requiring a reduced memory. More importantly, it is also demonstrated that these benefits accrue without any compromise in the attainable BER/BLER performance. We also present the novel concept of separating multiple users by means of user-specific channel codes, which is referred to as channel code division multiple access (CCDMA), and provide an example based on MLS LDPC codes. In particular, we circumvent the difficulty of having potentially high memory requirements, while ensuring that each user’s bits in the CCDMA system are equally protected. With regards to rateless channel coding, we propose a novel family of codes, which we refer to as reconfigurable rateless codes, that are capable of not only varying their code-rate but also to adaptively modify their encoding/decoding strategy according to the near-instantaneous channel conditions. We demonstrate that the proposed reconfigurable rateless codes are capable of shaping their own degree distribution according to the nearinstantaneous requirements imposed by the channel, but without any explicit channel knowledge at the transmitter. Additionally, a generalised transmit preprocessing aided closed-loop downlink multiple-input multiple-output (MIMO) system is presented, in which both the channel coding components as well as the linear transmit precoder exploit the knowledge of the channel state information (CSI). More explicitly, we embed a rateless code in a MIMO transmit preprocessing scheme, in order to attain near-capacity performance across a wide range of channel signal-to-ratios (SNRs), rather than only at a specific SNR. The performance of our scheme is further enhanced with the aid of a technique, referred to as pilot symbol assisted rateless (PSAR) coding, whereby a predetermined fraction of pilot bits is appropriately interspersed with the original information bits at the channel coding stage, instead of multiplexing pilots at the modulation stage, as in classic pilot symbol assisted modulation (PSAM). We subsequently demonstrate that the PSAR code-aided transmit preprocessing scheme succeeds in gleaning more information from the inserted pilots than the classic PSAM technique, because the pilot bits are not only useful for sounding the channel at the receiver but also beneficial for significantly reducing the computational complexity of the rateless channel decoder

A STUDY OF LINEAR ERROR CORRECTING CODES

Since Shannon's ground-breaking work in 1948, there have been two main development streams of channel coding in approaching the limit of communication channels, namely classical coding theory which aims at designing codes with large minimum Hamming distance and probabilistic coding which places the emphasis on low complexity probabilistic decoding using long codes built from simple constituent codes. This work presents some further investigations in these two channel coding development streams. Low-density parity-check (LDPC) codes form a class of capacity-approaching codes with sparse parity-check matrix and low-complexity decoder Two novel methods of constructing algebraic binary LDPC codes are presented. These methods are based on the theory of cyclotomic cosets, idempotents and Mattson-Solomon polynomials, and are complementary to each other. The two methods generate in addition to some new cyclic iteratively decodable codes, the well-known Euclidean and projective geometry codes. Their extension to non binary fields is shown to be straightforward. These algebraic cyclic LDPC codes, for short block lengths, converge considerably well under iterative decoding. It is also shown that for some of these codes, maximum likelihood performance may be achieved by a modified belief propagation decoder which uses a different subset of 7^ codewords of the dual code for each iteration. Following a property of the revolving-door combination generator, multi-threaded minimum Hamming distance computation algorithms are developed. Using these algorithms, the previously unknown, minimum Hamming distance of the quadratic residue code for prime 199 has been evaluated. In addition, the highest minimum Hamming distance attainable by all binary cyclic codes of odd lengths from 129 to 189 has been determined, and as many as 901 new binary linear codes which have higher minimum Hamming distance than the previously considered best known linear code have been found. It is shown that by exploiting the structure of circulant matrices, the number of codewords required, to compute the minimum Hamming distance and the number of codewords of a given Hamming weight of binary double-circulant codes based on primes, may be reduced. A means of independently verifying the exhaustively computed number of codewords of a given Hamming weight of these double-circulant codes is developed and in coiyunction with this, it is proved that some published results are incorrect and the correct weight spectra are presented. Moreover, it is shown that it is possible to estimate the minimum Hamming distance of this family of prime-based double-circulant codes. It is shown that linear codes may be efficiently decoded using the incremental correlation Dorsch algorithm. By extending this algorithm, a list decoder is derived and a novel, CRC-less error detection mechanism that offers much better throughput and performance than the conventional ORG scheme is described. Using the same method it is shown that the performance of conventional CRC scheme may be considerably enhanced. Error detection is an integral part of an incremental redundancy communications system and it is shown that sequences of good error correction codes, suitable for use in incremental redundancy communications systems may be obtained using the Constructions X and XX. Examples are given and their performances presented in comparison to conventional CRC schemes

Error-correction on non-standard communication channels

Many communication systems are poorly modelled by the standard channels assumed in the information theory literature, such as the binary symmetric channel or the additive white Gaussian noise channel. Real systems suffer from additional problems including time-varying noise, cross-talk, synchronization errors and latency constraints. In this thesis, low-density parity-check codes and codes related to them are applied to non-standard channels. First, we look at time-varying noise modelled by a Markov channel. A low-density parity-check code decoder is modified to give an improvement of over 1dB. Secondly, novel codes based on low-density parity-check codes are introduced which produce transmissions with Pr(bit = 1) ≠ Pr(bit = 0). These non-linear codes are shown to be good candidates for multi-user channels with crosstalk, such as optical channels. Thirdly, a channel with synchronization errors is modelled by random uncorrelated insertion or deletion events at unknown positions. Marker codes formed from low-density parity-check codewords with regular markers inserted within them are studied. It is shown that a marker code with iterative decoding has performance close to the bounds on the channel capacity, significantly outperforming other known codes. Finally, coding for a system with latency constraints is studied. For example, if a telemetry system involves a slow channel some error correction is often needed quickly whilst the code should be able to correct remaining errors later. A new code is formed from the intersection of a convolutional code with a high rate low-density parity-check code. The convolutional code has good early decoding performance and the high rate low-density parity-check code efficiently cleans up remaining errors after receiving the entire block. Simulations of the block code show a gain of 1.5dB over a standard NASA code

Advanced OFDM systems for terrestrial multimedia links

Recently, there has been considerable discussion about new wireless technologies and standards able to achieve high data rates. Due to the recent advances of digital signal processing and Very Large Scale Integration (VLSI) technologies, the initial obstacles encountered for the implementation of Orthogonal Frequency Division Multiplexing (OFDM) modulation schemes, such as massive complex multiplications and high speed memory accesses, do not exist anymore. OFDM offers strong multipath protection due to the insertion of the guard interval; in particular, the OFDM-based DVB-T standard had proved to offer excellent performance for the broadcasting of multimedia streams with bitrates over ten megabits per second in difficult terrestrial propagation channels, for fixed and portable applications. Nevertheless, for mobile scenarios, improving the receiver design is not enough to achieve error-free transmission especially in presence of deep shadow and multipath fading and some modifications of the standard can be envisaged. To address long and medium range applications like live mobile wireless television production, some further modifications are required to adapt the modulated bandwidth and fully exploit channels up to 24MHz wide. For these reasons, an extended OFDM system is proposed that offers variable bandwidth, improved protection to shadow and multipath fading and enhanced robustness thanks to the insertion of deep time-interleaving coupled with a powerful turbo codes concatenated error correction scheme. The system parameters and the receiver architecture have been described in C++ and verified with extensive simulations. In particular, the study of the receiver algorithms was aimed to achieve the optimal tradeoff between performances and complexity. Moreover, the modulation/demodulation chain has been implemented in VHDL and a prototype system has been manufactured. Ongoing field trials are demonstrating the ability of the proposed system to successfully overcome the impairments due to mobile terrestrial channels, like multipath and shadow fading. For short range applications, Time-Division Multiplexing (TDM) is an efficient way to share the radio resource between multiple terminals. The main modulation parameters for a TDM system are discussed and it is shown that the 802.16a TDM OFDM physical layer fulfills the application requirements; some practical examples are given. A pre-distortion method is proposed that exploit the reciprocity of the radio channel to perform a partial channel inversion achieving improved performances with no modifications of existing receivers