By Rolf Johannesson
Fundamentals of Convolutional Coding, moment Edition, considered as a bible of convolutional coding brings you a transparent and accomplished dialogue of the fundamental rules of this field
- Two new chapters on low-density parity-check (LDPC) convolutional codes and iterative coding
- Viterbi, BCJR, BEAST, checklist, and sequential interpreting of convolutional codes
- Distance houses of convolutional codes
- Includes a downloadable suggestions manual
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Extra resources for Fundamentals of Convolutional Coding
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The two output sequences v (1) = v0 v1 : : : and v (2) = v0 v1 : : : are (1) (2) (1) (2) interleaved by a serializer to form a single-output sequence v0 v0 v1 v1 : : : that is transmitted over the channel. For each information digit that enters the encoder, two channel digits are emitted. Thus, the code rate of this encoder is R = 1=2 bits/channel use. Assuming that the content of the register is zero at time t = 0, we notice that the two output sequences can be viewed as a convolution of the input sequence u and the two sequences 11100 : : : and 10100 : : :, respectively.
V 2K 1 1 + e1 1 + e2N K 1 b at the top of the column that The MD decoder decodes r to the codeword v contains r. 66) has the following standard array: 0000 1000 0100 0001 1011 0011 1111 1010 0110 1110 0010 0111 1101 0101 1001 1100 b = 1101. Suppose that r = 1001 is received. 11 An (N; K) binary linear code B can correct all error patterns in a set E if and only if these error patterns all lie in different cosets of FN 2 relative to B. Proof : Suppose that e and e0 are distinct error patterns in the same coset.
1 The code B has error-correcting capability t if and only if dmin > 2t. b as (one of) Proof : Suppose that dmin > 2t. Consider the decoder which chooses v the codeword(s) closest to r in Hamming distance (MD decoding). If r = v + e b must also satisfy dH (r; v b) t and e 2 Et , then dH (r; v) t. The decoder output v b must be at least as close to r as v is. 38) b = v and thus the decoding is correct. which implies that v Conversely, suppose that dmin 2t. 39) BLOCK CODES—A PRIMER 13 Thus, dH (v; r) = t and dH (v 0 ; r) = dmin t t (if t dmin ) and dH (v; r) = dmin and dH (v 0 ; r) = 0 (otherwise).