Unary error correction coding

Abstract

In this thesis, we introduce the novel concept of Unary Error Correction (UEC) coding. Our UEC code is a Joint Source and Channel Coding (JSCC) scheme conceived for performing both the compression and error correction of multimedia information during its transmission from an encoder to a decoder. The UEC encoder generates a bit sequence by concatenating and encoding unary codewords, while the decoder operates on the basis of a trellis that has only a modest complexity, even when the source symbol values are selected from a set having an infinite cardinality, such as the set of all positive integers. This trellis is designed so that the transitions between its states are synchronous with the transitions between the consecutive unary codewords in the concatenated bit sequence. This allows the UEC decoder to exploit any residual redundancy that remains following UEC encoding for the purpose of error correction by using the classic Bahl, Cocke, Jelinek and Raviv (BCJR) algorithm. Owing to this, the UEC code is capable of mitigating any potential capacity loss, hence facilitating near-capacity operation, even when the cardinality of the symbol value set is infinite.

We investigate the applications, characteristics and performance of the UEC code in the context of digital telecommunications. Firstly, we propose an adaptive UEC design for expediting the decoding process. By concatenating the UEC code with a turbo code, we conceive a three-stage concatenated adaptive iterative decoding technique. A Three-Dimensional (3D) EXtrinsic Information Transfer (EXIT) chart technique is proposed for both controlling the dynamic adaptation of the UEC trellis decoder, as well as for controlling the activation order between the UEC decoder and the turbo decoder. Secondly, we develop an irregular UEC design for ‘nearer-capacity’ operation. The irregular scheme employs different UEC parametrizations for the coding of different subsets of each message frame, operating on the basis of a single irregular trellis having a novel structure. This allows the irregularity to be controlled on a fine-grained bit-by-bit basis, rather than on a symbol-by-symbol basis. Hence, nearer-to-capacity operation is facilitated by exploiting this fine-grained control of the irregularity. Thirdly, we propose a learning-aided UEC design for transmitting symbol values selected from unknown and non-stationary probability distributions. The learning-aided UEC scheme is capable of heuristically inferring the source symbol distribution, hence eliminating the requirement of any prior knowledge of the symbol occurrence probabilities at either the transmitter or the receiver. This is achieved by inferring the source distribution based on the received symbols and by feeding this information back to the decoder. In this way, the quality of the recovered symbols and the estimate of the source distribution can be gradually improved in successive frames, hence allowing reliable near-capacity operation to be achieved, even if the source is unknown and non-stationary.

Finally, we demonstrate that the research illustrated in this thesis can be extended in several directions, by highlighting a number of opportunities for future work. The techniques proposed for enhancing the UEC code can be extended to the Rice Error Correction (RiceEC) code, to the Elias Gamma Error Correction (EGEC) code and to the Exponential Golomb Error Correction (ExpGEC) code. In this way, our UEC scheme may be extended to the family of universal error correction codes, which facilitate the nearcapacity transmission of infinite-cardinality symbol alphabets having any arbitrary monotonic probability distribution, as well as providing a wider range of applications. With these benefits, this thesis may contribute to future standards for the reliable near-capacity transmission of multimedia information, having significant technical and economic impact.

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Identifiers

ORCID for Lajos Hanzo: orcid.org/0000-0002-2636-5214

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