By Andre Neubauer
Probably the most very important key applied sciences for electronic communique platforms in addition to garage media is coding conception. It offers a method to transmit info throughout time and area over noisy and unreliable conversation channels. Coding concept: Algorithms, Architectures and purposes offers a concise evaluate of channel coding thought and perform, in addition to the accompanying sign processing architectures. The ebook is exclusive in providing algorithms, architectures, and purposes of coding idea in a unified framework. It covers the fundamentals of coding thought earlier than relocating directly to talk about algebraic linear block and cyclic codes, faster codes and occasional density parity money codes and space-time codes. Coding thought offers algorithms and architectures used for enforcing coding and interpreting suggestions in addition to coding schemes utilized in perform particularly in conversation platforms.
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Additional info for Coding Theory: Algorithms, Architectures and Applications
3: Encoding, transmission and decoding of an (n, k) block code the number of code words is given by q k . Since each entry carries n q-nary symbols, the total size of the table is n q k . The size of the table grows exponentially with increasing information word length k. For codes with a large number of code words – corresponding to a large information word length k – a coding scheme based on a table look-up procedure is inefﬁcient owing to the large memory size needed. For that reason, further algebraic properties are introduced in order to allow for a more efﬁcient encoder architecture of an (n, k) block code.
8 These errors cannot be detected. In general, the (n − k)-dimensional syndrome sT = H eT of a linear (n, k) block code B(n, k, d) corresponds to n − k scalar equations for the determination of the n-dimensional error vector e. The matrix equation s T = H eT does not uniquely deﬁne the error vector e. All vectors e with H eT = sT form a set, the so-called coset of the k-dimensional subspace B(n, k, d) in the ﬁnite vector space Fnq . This coset has q k elements. For an error-correcting q-nary block code B(n, k, d) and a given 8 This property directly follows from the linearity of the block code B(n, k, d).
K In the following, a q-nary channel code B ∈ Fnq with M code words b1 , b2 , . . , bM in the code space Fnq is considered. Let bj be the transmitted code word. Owing to the noisy channel, the received word r may differ from the transmitted code word bj . 6 is to decode the transmitted code word based on the sole knowledge of r with minimal word error probability perr . ˆ This decoding step can be written according to the decoding rule r → bˆ = b(r). For hard-decision decoding the received word r is an element of the discrete code space F nq .
Coding Theory: Algorithms, Architectures and Applications by Andre Neubauer