Generalized sphere-packing bound for subblock-constrained codes

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-compositi...

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Bibliographic Details
Main Authors: Kiah, Han Mao, Tandon, Anshoo, Motani, Mehul
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2022
Subjects:
Online Access:https://hdl.handle.net/10356/159500
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Institution: Nanyang Technological University
Language: English
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Summary: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.