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Dr Jing Cai PhD

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A Study of Erasure Correcting Codes

This work focus on erasure codes, particularly those that of high performance, and the related decoding algorithms, especially with low computational complexity. The work is composed of different pieces, but the main components are developed within the following two main themes.


Ideas of message passing are applied to solve the erasures after the transmission. Efficient matrix-representation of the belief propagation (BP) decoding algorithm on the BEC is introduced as the recovery algorithm. Gallager's bit-flipping algorithm are further developed into the guess and multi-guess algorithms especially for the application to recover the unsolved erasures after the recovery algorithm.



A novel maximum-likelihood decoding algorithm, the In-place algorithm, is proposed with a reduced computational complexity. A further study on the marginal number of correctable erasures by the In-place algorithm determines a lower bound of the average number of correctable erasures. Following the spirit in search of the most likable codeword based on the received vector, we propose a new branch-evaluation-search-on-the-code-tree (BESCT) algorithm, which is powerful enough to approach the ML performance for all linear block codes.



To maximize the recovery capability of the In-place algorithm in network transmissions, we propose the product packetisation structure to reconcile the computational complexity of the In-place algorithm. Combined with the proposed product packetisation structure, the computational complexity is less than the quadratic complexity bound. We then extend this to application of the Rayleigh fading channel to solve the errors and erasures. By concatenating an outer code, such as BCH codes, the product-packetised RS codes have the performance of the hard-decision In-place algorithm significantly better than that of the soft-decision iterative algorithms on optimally designed LDPC codes.

Dr Jing Cai

Director of studies: Prof. Martin Tomlinson
Other supervisors: Dr Marcel Ambroze, Dr Mohammed Zaki Ahmed

Journal papers

Analysis of the distribution of the number of erasures correctable by a binary linear code and the link to low-weight codewords
Tomlinson M, Tjhai CJ, Cai J, Ambroze MA
IET Communications, Volume 1, Issue 3, pp. 539-548, 2007
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1 Journal papers

Conference papers

Extended optimum decoding for LDPC codes based on exhaustive tree search algorithm
Yang L, Tomlinson M, Ambroze MA, Cai J
2010 IEEE International Conference on Communication Systems (ICCS), Singapore, 17-19 Nov, ISBN: 978-1-4244-7005-1, pp208 - 212, 2010
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A tree-based ML decoding algorithm with adaptive thresholding
Cai J, Tomlinson M, Tjhai CJ, Yang L
2010 IEEE International Conference on Communication Systems (ICCS), Singapore, 17-19 Nov, ISBN: 978-1-4244-7005-1, pp223 - 227, 2010
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Advances in Iterative Decoding and Maximum Likelihood Decoding for the Packet Network with Comparisons to Fountain Codes over the Erasure Channel
Cai J, Tomlinson M, Tjhai CJ, Ambroze MA, Ahmed MZ
Proceedings of the 4th International Symposium on Turbo Codes & Related Topics; 6th International ITG-Conference on Source and Channel Coding, Munich, Germany, 3-7 April, 2006
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Comparison of Concatenated Reed-Solomon Coding with Hard-decision to Soft-decision LDPC Coding for the Rayleigh Fading Channel
Cai J, Tomlinson M, Tjhai CJ, Ambroze MA, Ahmed MZ
IEEE Information Theory Workshop, ITW 06, Chengdu, China, 22-26 Oct, pp.135-139, 2006
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Analysis on Decoding Algorithms Based on Sectionalised Trellises of Block Codes and Their Dual
Cai J, Ambroze MA
Proceedings of the 2005 Postgraduate Research Conference in Electronics, Photonics, Communications and Networks, and Computing Science (PREP'05), Lancaster, UK, March, 2005
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Erasure correcting codes, network congestion, multicast and broadcast
Cai J, Tjhai CJ, Tomlinson M, Ambroze MA, Ahmed MZ
Proceedings of the 4th IASTED International Conference Communication Systems and Networks, Benidorm, Spain, 12-14 Sep, pp224–229, 2005
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6 Conference papers

Patents granted

A system for the correction of missing or deleted symbols
Tomlinson M, Cai J, Tjhai CJ, Ambroze MA, Ahmed MZ
Intellectual Property Office, UK Patent GB2421599, 2006
Filed: 22/12/2004; A Published: 28/06/2006; B Published: 08/10/2008
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1 Patents granted

Patents filed

Detection System and Method for Railway Track Circuits Using BPSK Modulated Coding
Radmore M, Cai J, Stewart K, Smith JP, Millar A
European Patent Office, EU Patent EP2100792A1, 2009
Filed: 11/03/2008; Published: 16/09/2009
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1 Patents filed

Presentations

Developing a new Train Detection system - Can Industry and Academia work together?
Millar A, Radmore M, Cai J
IET Invited Presentation, 14 May, University of Plymouth, 2008
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1 Presentations

10 publication(s) - all categories.