Closed-Form Approximation of Maximum Free Distance for Binary Block Codes
Closed-Form Approximation of Maximum Free Distance for Binary Block Codes
We devise an analytically simple as well as invertible approximate expression, which describes the relation between the maximum free distance of a binary code and the corresponding maximum attainable code-rate. For example, for a half-rate, length-128 binary code the known bounds limit the maximum attainable free distance to $16<d(n=128,r=0.5)<32$, while our solution yields $d(n=128,r=0.5)\approx 22$. The results provided may be utilized for the design and characterization of efficient coding schemes.
coding rate, free distance, upper bound, binary code, coding theory
Akhtman, Jos
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Bonello, Nicholas
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Maunder, Robert G.
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Hanzo, Lajos
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20 September 2009
Akhtman, Jos
6f612df7-9c17-4351-8340-5171fd174330
Bonello, Nicholas
77f072ac-4497-40d5-a916-d3cc5689c102
Maunder, Robert G.
76099323-7d58-4732-a98f-22a662ccba6c
Hanzo, Lajos
66e7266f-3066-4fc0-8391-e000acce71a1
Akhtman, Jos, Bonello, Nicholas, Maunder, Robert G. and Hanzo, Lajos
(2009)
Closed-Form Approximation of Maximum Free Distance for Binary Block Codes.
VTC'09 Fall, Anchorage, Alaska, United States.
20 - 23 Sep 2009.
(doi:10.1109/VETECF.2009.5378953).
Record type:
Conference or Workshop Item
(Paper)
Abstract
We devise an analytically simple as well as invertible approximate expression, which describes the relation between the maximum free distance of a binary code and the corresponding maximum attainable code-rate. For example, for a half-rate, length-128 binary code the known bounds limit the maximum attainable free distance to $16<d(n=128,r=0.5)<32$, while our solution yields $d(n=128,r=0.5)\approx 22$. The results provided may be utilized for the design and characterization of efficient coding schemes.
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Published date: 20 September 2009
Additional Information:
Event Dates: 20–23 September 2009
Venue - Dates:
VTC'09 Fall, Anchorage, Alaska, United States, 2009-09-20 - 2009-09-23
Keywords:
coding rate, free distance, upper bound, binary code, coding theory
Organisations:
Southampton Wireless Group
Identifiers
Local EPrints ID: 267544
URI: http://eprints.soton.ac.uk/id/eprint/267544
PURE UUID: 3d9810ab-a135-479f-91ff-9d2034265d08
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Date deposited: 10 Jun 2009 16:18
Last modified: 18 Mar 2024 03:09
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Contributors
Author:
Jos Akhtman
Author:
Nicholas Bonello
Author:
Robert G. Maunder
Author:
Lajos Hanzo
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