Design of Packet-Based Block Codes with Shift Operators

• Main Authors: Ilow Jacek, Al-Shaikhi Ali
• Format: Article
• Language: English
• Published: SpringerOpen 2010-01-01
• Series: EURASIP Journal on Wireless Communications and Networking
• Online Access: http://jwcn.eurasipjournals.com/content/2010/263210

<p/> <p>This paper introduces packet-oriented block codes for the recovery of lost packets and the correction of an erroneous single packet. Specifically, a family of systematic codes is proposed, based on a Vandermonde matrix applied to a group of <inline-formula> <graphic file="1687-1499-2010-263210-i1.gif"/></inline-formula> information packets to construct <inline-formula> <graphic file="1687-1499-2010-263210-i2.gif"/></inline-formula> redundant packets, where the elements of the Vandermonde matrix are bit-level right arithmetic shift operators. The code design is applicable to packets of any size, provided that the packets within a block of <inline-formula> <graphic file="1687-1499-2010-263210-i3.gif"/></inline-formula> information packets are of uniform length. In order to decrease the overhead associated with packet padding using shift operators, non-Vandermonde matrices are also proposed for designing packet-oriented block codes. An efficient matrix inversion procedure for the off-line design of the decoding algorithm is presented to recover lost packets. The error correction capability of the design is investigated as well. The decoding algorithm, based on syndrome decoding, to correct a single erroneous packet in a group of <inline-formula> <graphic file="1687-1499-2010-263210-i4.gif"/></inline-formula> received packets is presented. The paper is equipped with examples of codes using different parameters. The code designs and their performance are tested using Monte Carlo simulations; the results obtained exhibit good agreement with the corresponding theoretical results.</p>