On Rate-Compatible Punctured Turbo Codes Design
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On Rate-Compatible Punctured Turbo Codes Design Fulvio Babich Dipartimento di Elettrotecnica, Elettronica e Informatica (DEEI), Universit`a di Trieste, via A. Valerio 10, 34127 Trieste, Italy Email: [email protected]
Guido Montorsi Dipartimento di Elettronica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy Email: [email protected]
Francesca Vatta Dipartimento di Elettrotecnica, Elettronica e Informatica (DEEI), Universit`a di Trieste, via A. Valerio 10, 34127 Trieste, Italy Email: [email protected] Received 30 September 2003; Revised 25 June 2004 We propose and compare some design criteria for the search of good systematic rate-compatible punctured turbo code (RCPTC) families. The considerations presented by S. Benedetto et al. (1998) to find the “best” component encoders for turbo code construction are extended to find good rate-compatible puncturing patterns for a given interleaver length N. This approach is shown to lead to codes that improve over previous ones, both in the maximum-likelihood sense (using transfer function bounds) and in the iterative decoding sense (through simulation results). To find simulation and analytical results, the coded bits are transmitted over an additive white Gaussian noise (AWGN) channel using an antipodal binary modulation. The two main applications of this technique are its use in hybrid incremental ARQ/FEC schemes and its use to achieve unequal error protection of an information sequence. Keywords and phrases: turbo codes, iterative decoding, rate-compatible punctured codes.
1.
INTRODUCTION
In this paper, we propose a new criterion for the choice of the puncturing patterns, based on the analytical technique introduced in [1], that leads to systematic rate-compatible codes improving over known ones with respect to both maximumlikelihood and iterative decoding criteria. The concept of rate-compatible codes has been presented for the first time in [2], where a particular family of convolutional codes, called in the paper rate-compatible punctured convolutional codes, is obtained by adding a ratecompatibility restriction to the puncturing rule. This restriction requires that the rates are organized in a hierarchy, where all coded bits of a higher-rate code are used by all lower-rate codes; or, in other words, the high-rate codes are embedded into the lower-rate codes of the family. The concept of ratecompatible codes has been extended to turbo codes in [3, 4]. Design criteria for the puncturing patterns have successively appeared in [5, 6]. The two main applications of this technique are the following.
Modified type-II automatic repeat request/forward-error correction (ARQ/FEC) schemes The principle of this hybrid ARQ/FEC scheme [7] is not to repeat information or parity bits if the transmission is unsuccessful, as in previous type-II ARQ/FEC schemes, but to transmit additional code bits of a lower-rate code, until the code is powerful enough to achieve error free decoding. Namely, if the higher-rate codes are not sufficiently powerful to correct chan
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