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

Exponential Golomb and Rice Error Correction codes for generalized near-capacity joint source and channel coding
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.
1-20
Brejza, Matthew
a761342e-e140-45a7-ad48-095a6628af17
Wang, Tao
dd7d278c-abe5-46f4-9fa3-39e5629d43d7
Zhang, Wenbo
949b3fcf-0a51-4575-b6de-b4029bfbaf3f
Al-Khalili, David
5f484fba-7d29-4105-856b-9bd34fc62424
Maunder, Robert
76099323-7d58-4732-a98f-22a662ccba6c
Al-Hashimi, Bashir
0b29c671-a6d2-459c-af68-c4614dce3b5d
Hanzo, Lajos
66e7266f-3066-4fc0-8391-e000acce71a1
Brejza, Matthew
a761342e-e140-45a7-ad48-095a6628af17
Wang, Tao
dd7d278c-abe5-46f4-9fa3-39e5629d43d7
Zhang, Wenbo
949b3fcf-0a51-4575-b6de-b4029bfbaf3f
Al-Khalili, David
5f484fba-7d29-4105-856b-9bd34fc62424
Maunder, Robert
76099323-7d58-4732-a98f-22a662ccba6c
Al-Hashimi, Bashir
0b29c671-a6d2-459c-af68-c4614dce3b5d
Hanzo, Lajos
66e7266f-3066-4fc0-8391-e000acce71a1

Brejza, Matthew, Wang, Tao, Zhang, Wenbo, Al-Khalili, David, Maunder, Robert, Al-Hashimi, Bashir and Hanzo, Lajos (2016) Exponential Golomb and Rice Error Correction codes for generalized near-capacity joint source and channel coding. IEEE Access, 1-20. (doi:10.1109/ACCESS.2016.2584982).

Record type: Article

Abstract

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.

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Accepted/In Press date: 16 June 2016
Published date: 24 June 2016
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 397286
URI: https://eprints.soton.ac.uk/id/eprint/397286
PURE UUID: f28a6d0a-db7f-4517-ad11-5e09f7509bcb
ORCID for Robert Maunder: ORCID iD orcid.org/0000-0002-7944-2615
ORCID for Lajos Hanzo: ORCID iD orcid.org/0000-0002-2636-5214

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Date deposited: 23 Jun 2016 20:13
Last modified: 06 Jun 2018 13:15

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Contributors

Author: Matthew Brejza
Author: Tao Wang
Author: Wenbo Zhang
Author: David Al-Khalili
Author: Robert Maunder ORCID iD
Author: Lajos Hanzo ORCID iD

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