Near-capacity joint source and channel coding of symbol values from an infinite source set using Elias Gamma Error correction codes

In this paper we propose a novel low-complexity Joint Source and Channel Code (JSCC), which we refer to as the Elias Gamma Error Correction (EGEC) code. Like the recently-proposed Unary Error Correction (UEC) code, this facilitates the practical near-capacity transmission of symbol values that are randomly selected from a set having an infinite cardinality, such as the set of all positive integers. However, in contrast to the UEC code, our EGEC code is a universal code, facilitating the transmission of symbol values that are randomly selected using any monotonic probability distribution. When the source symbols obey a particular zeta probability distribution, our EGEC scheme is shown to offer a 3.4 dB gain over a UEC benchmarker, when Quaternary Phase Shift Keying (QPSK) modulation is employed for transmission over an uncorrelated narrowband Rayleigh fading channel. In the case of another zeta probability distribution, our EGEC scheme offers a 1.9 dB gain over a Separate Source and Channel Coding (SSCC) benchmarker

Exponential Golomb and Rice Error Correction codes for generalized near-capacity joint source and channel coding

The recently proposed Unary Error Correction (UEC) and Elias Gamma Error Correction (EGEC) codes facilitate the near-capacity Joint Source and Channel Coding (JSCC) of symbol values selected from large alphabets at a low complexity. Despite their large alphabet, these codes were only designed for a limited range of symbol value probability distributions. In this paper, we generalize the family of UEC and EGEC codes to the class of Rice and Exponential Golomb (ExpG) Error Correction (RiceEC and ExpGEC) codes, which have a much wider applicability, including the symbols produced by the H.265 video codec, the letters of the English alphabet and in fact any arbitrary monotonic unbounded source distributions. Furthermore, the practicality of the proposed codes is enhanced to allow a continuous stream of symbol values to be encoded and decoded using only fixed-length system components. We explore the parameter space to offer beneficial trade-offs between error correction capability, decoding complexity, as well as transmission-energy, -duration and -bandwidth over a wide range of operating conditions. In each case, we show that our codes offer significant performance improvements over the best of several state-of-the-art benchmarkers. In particular, our codes achieve the same error correction capability, as well as transmissionenergy, -duration and -bandwidth as a Variable Length Error- Correction (VLEC) code benchmarker, while reducing the decoding complexity by an order of magnitude. In comparison with the best of the other JSCC and Separate Source and Channel Coding (SSCC) benchmarkers, our codes consistently offer E_b/N_0 gains of between 0.5 dB and 1.0 dB which only appear to be modest, because the system operates close to capacity. These improvements are achieved for free, since they are not achieved at the cost of increasing transmission-energy, -duration, -bandwidth or decoding complexity

A unary error correction code for the near-capacity joint source and channel coding of symbol values from an infinite set

A novel Joint Source and Channel Code (JSCC) is proposed, which we refer to as the Unary Error Correction (UEC) code. Unlike existing JSCCs, our UEC facilitates the practical encoding of symbol values that are selected from a set having an infinite cardinality. Conventionally, these symbols are conveyed using Separate Source and Channel Codes (SSCCs), but we demonstrate that the residual redundancy that is retained following source coding results in a capacity loss, which is found to have a value of 1.11 dB in a particular practical scenario. By contrast, the proposed UEC code can eliminate this capacity loss, or reduce it to an infinitesimally small value. Furthermore, the UEC code has only a moderate complexity, facilitating its employment in practical low-complexity applications

Adaptive iterative detection for expediting the convergence of a serially concatenated unary error correction decoder, turbo decoder and an iterative demodulator

Unary Error Correction (UEC) codes constitute a recently proposed Joint Source and Channel Code (JSCC) family, conceived for alphabets having an infinite cardinality, whilst out-performing previously used Separate Source and Channel Codes (SSCCs). UEC based schemes rely on an iterative decoding process, which involves three decoding blocks when concatenated with a turbo code. Owing to this, following the activation of one of the three blocks, the next block to be activated must be chosen from the other two decoding block options. Furthermore, the UEC decoder offers a number of decoding options, allowing its complexity and error correction capability to be dynamically adjusted. It has been shown that iterative decoding convergence can be expedited by activating the specific decoding option that offers the highest Mutual Information (MI) improvement to computational complexity ratio. This paper introduces an iterative demodulator, which is shown to improve the associated error correction performance, while reducing the overall iterative decoding complexity. The challenge is that the iterative demodulator has to forward its soft-information to the other two iterative decoding blocks, and hence the corresponding MI improvements cannot be compared on a like-for-like basis. Additionally, we also propose a method of eliminating the logarithmic calculations from the adaptive iterative decoding algorithm, hence further reducing its implementational complexity without impacting its error correcting performance

Iterative decoding for error resilient wireless data transmission

Both turbo codes and LDPC codes form two new classes of codes that offer energy efficiencies close to theoretical limit predicted by Claude Shannon. The features of turbo codes include parallel code catenation, recursive convolutional encoders, punctured convolutional codes and an associated decoding algorithm. The features of LDPC codes include code construction, encoding algorithm, and an associated decoding algorithm. This dissertation specifically describes the process of encoding and decoding for both turbo and LDPC codes and demonstrates the performance comparison between theses two codes in terms of some performance factors. In addition, a more general discussion of iterative decoding is presented. One significant contribution of this dissertation is a study of some major performance factors that intensely contribute in the performance of both turbo codes and LDPC codes. These include Bit Error Rate, latency, code rate and computational resources. Simulation results show the performance of turbo codes and LDPC codes under different performance factors

On Coding and Detection Techniques for Two-Dimensional Magnetic Recording

Edited version embargoed until 15.04.2020 Full version: Access restricted permanently due to 3rd party copyright restrictions. Restriction set on 15/04/2019 by AS, Doctoral CollegeThe areal density growth of magnetic recording systems is fast approaching the superparamagnetic limit for conventional magnetic disks. This is due to the increasing demand for high data storage capacity. Two-dimensional Magnetic Recording (TDMR) is a new technology aimed at increasing the areal density of magnetic recording systems beyond the limit of current disk technology using conventional disk media. However, it relies on advanced coding and signal processing techniques to achieve areal density gains. Current state of the art signal processing for TDMR channel employed iterative decoding with Low Density Parity Check (LDPC) codes, coupled with 2D equalisers and full 2D Maximum Likelihood (ML) detectors. The shortcoming of these algorithms is their computation complexity especially with regards to the ML detectors which is exponential with respect to the number of bits involved. Therefore, robust low-complexity coding, equalisation and detection algorithms are crucial for successful future deployment of the TDMR scheme. This present work is aimed at finding efficient and low-complexity coding, equalisation, detection and decoding techniques for improving the performance of TDMR channel and magnetic recording channel in general. A forward error correction (FEC) scheme of two concatenated single parity bit systems along track separated by an interleaver has been presented for channel with perpendicular magnetic recording (PMR) media. Joint detection decoding algorithm using constrained MAP detector for simultaneous detection and decoding of data with single parity bit system has been proposed. It is shown that using the proposed FEC scheme with the constrained MAP detector/decoder can achieve a gain of up to 3dB over un-coded MAP decoder for 1D interference channel. A further gain of 1.5 dB was achieved by concatenating two interleavers with extra parity bit when data density along track is high. The use of single bit parity code as a run length limited code as well as an error correction code is demonstrated to simplify detection complexity and improve system performance. A low-complexity 2D detection technique for TDMR system with Shingled Magnetic Recording Media (SMR) was also proposed. The technique used the concatenation of 2D MAP detector along track with regular MAP detector across tracks to reduce the complexity order of using full 2D detection from exponential to linear. It is shown that using this technique can improve track density with limited complexity. Two methods of FEC for TDMR channel using two single parity bit systems have been discussed. One using two concatenated single parity bits along track only, separated by a Dithered Relative Prime (DRP) interleaver and the other use the single parity bits in both directions without the DRP interleaver. Consequent to the FEC coding on the channel, a 2D multi-track MAP joint detector decoder has been proposed for simultaneous detection and decoding of the coded single parity bit data. A gain of up to 5dB was achieved using the FEC scheme with the 2D multi-track MAP joint detector decoder over un-coded 2D multi-track MAP detector in TDMR channel. In a situation with high density in both directions, it is shown that FEC coding using two concatenated single parity bits along track separated by DRP interleaver performed better than when the single parity bits are used in both directions without the DRP interleaver.9mobile Nigeri