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CeRapiInvoke() operates in one of two modes, depending on the value of the IRAPIStream ** parameter to the function. If this parameter is set equal to NULL, the function returns after all processing is completed on the CE side. This is called synchronous behavior, or block mode. The advantage of block mode is that it s simple to implement, but it s also slower and less flexible than the asynchronous stream mode. If the ppIRAPIStream parameter contains a valid pointer to an interface, then CeRapiInvoke() operates in stream mode. In stream mode, the desktop side and the application can communicate during the CE side processing, sending data of arbitrary size back and forth via the RAPI stream interface. We use block mode here, as the CE application and the desktop aren t exchanging data.

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Many references appear throughoutthis chapter; see especially Section 15.1. Tanner graphs and codes built using graphs are discussed in [330]. On the analysis of LDPC codes, the paper [290] is highly recommended, which uses density evolution. Density evolution is also discussed in [51] (our discussion comes from there) and from [15]. See also [74]. The EXIT chart for turbo codes was presented in [334,335]. The discussion of irregular LDPC codes comes from [292]. See also [212]. One of the potential drawbacks to LDPC codes is the large number of decoding iterations that may be required, resulting in increased latency and decoding hardware complexity. An approach to reduce the number of iterations is presented in [47,62], in which the messages around a cycle in the Tanner graph establish an eigenvalue problem or a least-squared problem. Our discussion of encoding comes from [289]. Another class of approaches is based on iterative use of the decoding algorithm in the encoding process. This could allow for the same hardware to be used for both encoding and decoding. These approaches are described in [135]. Using the sum-product decoder on general matrices is explored in [245]. An excellent resource on material related to turbo codes, LDPC codes, and iterative decoding in general is the February 2001 issue of the IEEE Transactions on Information Theory, which contains many articles in addition to those articles cited here. Interesting results on the geometry of the iterative decoding process are in [156]. Repeat accumulate codes are presented in [167]. Our presentation has benefited from the discussion in [151.

28 N

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Cost $1,900,000 $80,000,000 1.00% $800,000 10.00% 5 $211,000 $2,111,000

5.77 [373] Let ( f ( x ) ,h(x)) be the ideal I c GF(2)[x]/(xn - 1) formed by all linear combinations of the form a ( x ) f ( x ) b ( x ) g ( x ) , where a(x),b(x) E GF(2)[x]/(xn - 1). By Theorem4.1, I is principal. Determine the generator for I . 5.78 Let A ( z ) = x r = o A n z n and B(z) = Bnzn be generating functions and let C ( z ) = A ( z ) B ( z ) .Using the property of a formal derivative that A'(z) = CEO nAnz"-l, show that Ai(z), show that C'(z) = A'(z)B(z) A ( z ) B ' ( z ) . extension, show that if C ( z ) = By

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class Customer @@no_of_customers=0 def initialize(id, name, addr) @cust_id=id @cust_name=name @cust_addr=addr end def displayDetails() puts Customer id #@cust_id puts Customer name #@cust_name puts Customer address #@cust_addr end def total_no_of_customers() @@no_of_customers += 1 puts Total number of customers: #@@no_of_customers end end

Arabic numbers Roman numerals (upper- or lowercase) Letters (upper- or lowercase) Numerous other language-speci c numbers/letters