Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/159500
Title: Generalized sphere-packing bound for subblock-constrained codes
Authors: Kiah, Han Mao
Tandon, Anshoo
Motani, Mehul
Keywords: Science::Mathematics
Issue Date: 2020
Source: Kiah, H. M., Tandon, A. & Motani, M. (2020). Generalized sphere-packing bound for subblock-constrained codes. IEEE Transactions On Information Theory, 67(1), 187-199. https://dx.doi.org/10.1109/TIT.2020.3027847
Project: MOE2019-T2-2-171
Journal: IEEE Transactions on Information Theory
Abstract: We apply the generalized sphere-packing bound to two classes of subblock-constrained codes. À la Fazeli et al. (2015), we make use of automorphisms to significantly reduce the number of variables in the associated linear programming problem. In particular, we study binary constant subblock-composition codes (CSCCs), characterized by the property that the number of ones in each subblock is constant, and binary subblock energy-constrained codes (SECCs), characterized by the property that the number of ones in each subblock exceeds a certain threshold. For CSCCs, we show that the optimization problem is equivalent to finding the minimum of N variables, where N is independent of the number of subblocks. We then provide closed-form solutions for the generalized sphere-packing bounds for t-error correcting CSCCs for $\text {t}\in \{1,2,3\}$. For SECCs, we provide closed-form solutions for the generalized sphere-packing bounds for single errors in certain special cases. We also obtain improved bounds on the optimal asymptotic rate for CSCCs and SECCs, and provide numerical examples to highlight the improvement.
URI: https://hdl.handle.net/10356/159500
ISSN: 0018-9448
DOI: 10.1109/TIT.2020.3027847
Schools: School of Physical and Mathematical Sciences 
Rights: © 2020 IEEE. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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