By Xinmiao Zhang
Error-correcting codes are ubiquitous. they're followed in virtually each sleek electronic verbal exchange and garage procedure, reminiscent of instant communications, optical communications, Flash stories, computing device tough drives, sensor networks, and deep-space probing. New-generation and rising functions call for codes with greater error-correcting strength. however, the layout and implementation of these high-gain error-correcting codes pose many demanding situations. and so they contain complicated mathematical computations, and mapping them on to frequently ends up in very excessive complexity.
VLSI Architectures for contemporary Error-Correcting Codes
serves as a bridge connecting developments in coding concept to functional implementations. rather than concentrating on circuit-level layout strategies, the e-book highlights built-in algorithmic and architectural adjustments that bring about nice advancements on throughput, silicon quarter requirement, and/or strength intake within the implementation.
The objective of this booklet is to supply a finished and systematic overview of obtainable options and architectures, so that it will be simply by way of procedure and designers to advance en/decoder implementations that meet error-correcting functionality and price necessities. This publication will be extensively utilized as a reference for graduate-level classes on VLSI layout and error-correcting coding. specific emphases are put on difficult- and soft-decision Reed-Solomon (RS) and Bose-Chaudhuri-Hocquenghem (BCH) codes, and binary and non-binary low-density parity-check (LDPC) codes. those codes are among the finest applicants for contemporary and rising functions as a result of their sturdy error-correcting functionality and reduce implementation complexity in comparison to different codes. to aid clarify the computations and en/decoder architectures, many examples and case experiences are included.
More importantly, discussions are supplied at the benefits and disadvantages of alternative implementation methods and architectures.
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Extra info for VLSI architectures for modern error-correcting codes
Folding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 26 30 34 Some fundamental concepts used in VLSI architecture design are first introduced in this chapter. Then brief discussions are given to pipelining, retiming, parallel processing, and folding, which are techniques that can be used to manipulate circuits to tradeoff speed, silicon area, and power consumption. These definitions and techniques are necessary to understand the error-correcting decoder designs introduced in later chapters.
Each edge is also associated with the same number of delay elements as in the corresponding data path. Fig. 2(a) shows the block diagram of a filter, and the corresponding DFG is illustrated in Fig. 2(b). Definition 21 (Cutset) A cutset is a set of edges, such that the graph becomes two disjoint parts when they are removed. 3 Cutset examples Definition 22 (Feed-forward cutset) If the edges in a cutset go in the same direction, then the cutset is called a feed-forward cutset. Example 16 In the DFG shown in Fig.
Scheme C α−1 = α254 = (((α7 )2 )4 )4 · ((α3 )2 )4 · (α3 )2 . Hence, the inversion over GF (28 ) can be also implemented by the architecture in Fig. 6. Compared to a general multiplier, the square, cube, and quartic operators are simpler. It has been shown in  that among the three non-iterative architectures shown in Figs. 6, the one according to Scheme A has the highest complexity for the inversion over GF (28 ) despite its more regular architecture. The one corresponding to Scheme C requires the least hardware and has the shortest critical path.
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