J. D. Andersen, "The TURBO coding scheme," Tech. Univ. Denmark, Lyngby, Denmark, Tech. Rep. IT-146, June 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... a random interleaver, as currently practiced (at least for long interleavers) yields excellent average performance with high probability; however, some of the bad input sequences escape transformation, so there remain a few low weight codewords that cause what has been called the error floor [6], 7] The error floor usually appears in the region of the bit error rate (BER) curve of turbo codes below , such that in order to further improve the BER by an order of magnitude, it is necessary to provide about a 1 dB enhancement in the signal to noise ratio (SNR) i.e. the error floor ....

J. D. Andersen, "The TURBO coding scheme," Tech. Univ. Denmark, Lyngby, Denmark, Tech. Rep. IT-146, June 1994.

....et al. 1] turbo codes with long frame lengths were shown to achieve bit error rate (BER) performance as low as 10 with a signal to noise ratio (SNR) less than 1 dB from capacity in the so called waterfall region of the BER curve. However, in the so called error floor region of the BER curve [2], 3] the slope becomes very shallow, making it difficult to achieve very small BERs without significantly increasing the SNR. The error floor is due to the presence of low weight codewords with small multiplicities, and thus for high SNRs a frame with decoded errors will typically have only a ....

J. D. Andersen, "The TURBO coding scheme," Tech. Univ. of Denmark, Lyngby, Rep. IT-146, June 1994.

.... The discovery of Turbo codes and the near capacity performance reported in [1] has stimulated a flurry of research e#orts to fully understand this new coding scheme [2] 43] Initially greeted with some skepticism, the original results were independently reproduced by several researchers [6] 7] [10] [11] 12] 13] and [30] Subsequently, recent research on Turbo codes has focused on understanding the reasons for their outstanding performance [8] 9] 16] 22] 24] 28] At this point, there are two fundamental questions regarding Turbo codes. First, does the iterative decoding ....

....results raises two issues regarding the performance of Turbo codes. First, what is it that allows Turbo codes to achieve a bit error rate (BER) of 10 5 at a signal to noise ratio (SNR) of E b N 0 =0.7 dB, which is only 0. 7dB from the Shannon limit Second, what causes the error floor [10], 13] that is, the flattening of the performance curve, for moderate to high SNR s Here, we endeavor to explain the performance of Turbo codes, and thus address these two issues, in terms of the code s distance spectrum. We do not attempt to address the many interesting questions concerning the ....

J. D. Andersen, The TURBO Coding Scheme, Report IT-146, Technical University of Denmark, June 1994.

....behavior performance nor an adequate comprehension of the role and relative importance of the PCCs ingredients (constituent codes and interleaver) have appeared so far. In terms of performance of PCCs, apart from the measurements on the chip [7] what is known is essentially due to simulation [5, 15, 8, 16, 17, 18], which, in itself, is not at all a simple task, as it requires a huge computer time to obtain reliable results down to bit error probabilities like 10 06 . As a consequence, a number of basic questions are still unanswered: 1. What is the performance of the ML decoder 2. What are the relative ....

Jakob Dahl Andersen. "The TURBO Coding Scheme". In Proceedings of ISIT'94, Trondheim, Norway, June 1994.

.... discovery of Turbo codes and the near capacity performance reported in [1] has stimulated a flurry of research efforts to fully understand this new coding scheme [2] 43] Initially greeted with some skepticism, the original results were independently reproduced by several researchers [6] 7] [10] [11] 12] 13] and [30] Subsequently, recent research on Turbo codes has focused on understanding the reasons for their outstanding performance [8] 9] 16] 22] 24] 28] At this point, there are two fundamental questions regarding Turbo codes. First, does the iterative decoding ....

....results raises two issues regarding the performance of Turbo codes. First, what is it that allows Turbo codes to achieve a bit error rate (BER) of 10 Gamma5 at a signal to noise ratio (SNR) of E b =N 0 = 0:7 dB, which is only 0. 7dB from the Shannon limit Second, what causes the error floor [10], 13] that is, the flattening of the performance curve, for moderate to high SNR s Here, we endeavor to explain the performance of Turbo codes, and thus address these two issues, in terms of the code s distance spectrum. We do not attempt to address the many interesting questions concerning the ....

J. D. Andersen, The TURBO Coding Scheme, Report IT-146, Technical University of Denmark, June 1994.

....used with turbo codes in [4] but the derivation presented was unnecessarily complex. To avoid an increase of the bit error ratio at low signal to noise ratios, the extrinsic information had to be divided by a heuristic formula. Also there was no detailed description of the interleaver design. In [24] the derivation of the MAP algorithm is similar to ours but the definitions of the state metrics # and # are different for a non recursive code than for a recursive code. Also the final formula to find the APP for recursive codes is more complicated. The algorithm as described here is also close ....

....in (2.10) it is useful to compute the following probability functions # i k (m) # P r (d k # i, S k # m, R k 1 ) 2.13) # i k (m) # P r (R N k#1 d k # i, S k # m) 2.14) where i is the value of the information bit at time k. These definitions are different from those used in [6, 24, 25] in the way that both # and # depend on the value of the information bit d k . This is very helpful later on when we can simplify the final relations to compute the Log Likelihood Ratio, L#d k ) Using Bayes rule, the joint probability from (2.10) can be rewritten as follows # i k (m) # P r ....

J. Andersen, "The turbo coding scheme," IEEE International Symposium on Information Theory, Trondheim, Norway, June 1994.

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