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The publisher and I want your feedback. After you have had a chance to use this book, please take a moment to visit the Hungry Minds, Inc. Web site to register your book and give us your comments. (See the my2cents.hungryminds.com page at the back of this book for more details.) Please be honest in your evaluation. If you thought a particular chapter didn t tell you enough, let me know. Of course, I would prefer to receive comments like This is the best book I ve ever read, or Thanks to this book, I was promoted and now make $90,000 a year. I get at least a dozen questions every day, via e-mail, from people who have read my books. I appreciate the feedback. Unfortunately, I simply don t have the time to reply to questions. Appendix A provides a good list of sources that can answer your questions. I also invite you to visit my Web site, which contains lots of Excel-related material. Despite the massive attempts to make this book completely accurate, a few errors have probably crept into its pages. My Web site includes a list of any such errors. The URL is

transmitting signaling link terminal until a positive acknowledgment for that signal unit is received. If a negative acknowledgment is received, then the transmission of new signal units is interrupted and those signal units which have been transmitted but not yet positively acknowledged (starting with that indicated by the negative acknowledgment) will be transmitted once, in the order in which they were rst transmitted. The preventive cyclic retransmission method is a noncompelled, positive acknowledgment, cyclic retransmission forward error correction system. A signal unit which has been transmitted is retained at the transmitting signaling unit terminal until a positive acknowledgment for that signaling unit is received. During the period when there are no new signal units to be transmitted, all signal units which have not been positively acknowledged are retransmitted cyclically. The forced retransmission procedure is de ned to ensure that forward error correction occurs in adverse conditions (e.g., degraded BER and/ or high-traf c loading). When a predetermined number of retained, unacknowledged signal units exist, the transmission of new signal units is retransmitted cyclically until the number of acknowledged signal units is reduced.

(5.11)

(a) A positive (semi) definite, c > 0 defini teo (b) A negative (semi) definite, c > 0 definite. (c) A positive (semi) definite, c (d) A negative (semi) definite, c

LDPC codes are usually designed to be linear and binary block codes In this case there is a generator matrix G that converts a message vector m into a code vector c by means of a matrix multiplication The corresponding parity check matrix H has the property that it is constructed with linearly independent row vectors that form the dual subspace of the subspace generated by the linearly independent row vectors of G This means that every code vector satis es the condition H c = 0 LDPC codes are designed by an appropriate construction of the corresponding parity check matrix H, which is characterized by being sparse.

According to the de nition given by Gallager, an LDPC code is denoted as CLDPC (n, s, v), where n is the code length, s is the number of 1 s per column, with in general s 3, and v is the number of 1 s per row If the rows of the parity check matrix are linearly independent then the code rate is equal to (v s)/v [4] Otherwise the code rate is n s /n, where s is the actual dimension of the row subspace generated by the parity check matrix H This relationship is obtained by counting the total number of 1 s per row, and then per column, giving that ns = (n k)v, which by algebraic manipulation leads to the expression for the code rate.

If the LDPC code is irregular, the numbers of 1 s per row v and/or per column s are not xed, and so the rate of the code is obtained by using the average values of these parameters The code construction proposed by Gallager allowed him to demonstrate the main properties of these codes: the error probability decreases exponentially with increasing code block length, and the minimum distance of the code also increases with increasing code length Tanner [7] generalized the Gallager construction, de ning the so-called bipartite graphs, where equations.

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