S. Pietrobon, "Implementation and Performance of a Serial MAP Decoder for use in an Iterative Turbo Decoder", Int. Symp. on Inform. Theory and its Applications, Sidney, NSW, Nov. 1994, pp. 1073-1077.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....is used [3] Although the MAP algorithm is highly data dominated, its memory optimization has never been treated extensively so far [3] 4] Also the organization of the decoding modules in the global decoder system has been mostly ignored. Existing solutions use a serial concatenation [5] 6] [7] or a suboptimal feedback loop over the modules [3] 7] We propose a more efficient structure for the entire turbo decoder by optimizing both the module and system level. Our module level optimizations result in a memory efficient algorithm organization, while the system level approach is based ....

....dominated, its memory optimization has never been treated extensively so far [3] 4] Also the organization of the decoding modules in the global decoder system has been mostly ignored. Existing solutions use a serial concatenation [5] 6] 7] or a suboptimal feedback loop over the modules [3] [7]. We propose a more efficient structure for the entire turbo decoder by optimizing both the module and system level. Our module level optimizations result in a memory efficient algorithm organization, while the system level approach is based on an intelligent way to implement the interleaving ....

S. Pietrobon, "Implementation and Performance of a Serial MAP Decoder for use in an Iterative Turbo Decoder", Int. Symp. on Inform. Theory and its Applications, Sidney, NSW, Nov. 1994, pp. 1073-1077.

.... or serial) seems to be less important [30] Independently, in 1992 93 Lodge et al. invented the iterative decoding of product codes using simple block and convolutional codes [17, 18] In the works by Berrou and Lodge, two BCJR algorithms [1] matched to the constituent codes were applied [24, 21, 25, 22], passing reliability information iteratively between the constituent decoders [5, 6, 30, 17, 18] Also in common was the observation that for systematic codes the BCJR input data can be factored into three (ideally) independent terms and that data should not been used twice in each decoding step: ....

....or accepted, see Item 6. iii) It is irrelevant whether the extrinsic information is Gaussian distributed or not. 2. We found it mandatory (and not just convenient) to implement the MAP decoders in the log domain (called Log MAP or dual generalized VA) in order to avoid numerical problems [24, 21, 25, 31, 22]. 3. Given the low extra effort and a noticeable gain at low SNR when using Log MAPs (instead of Sub MAPs, see Item 7) we warmly recommend to use an optimal constituent decoder [24, 21, 25, 31, 22] 4. Then, we always observed a decreasing BER when increasing the number of iterations, until a ....

[Article contains additional citation context not shown here]

S.S. Pietrobon, "Implementation and performance of a serial MAP decoder for use in an iterative turbo decoder," in Proc. IEEE Int. Symp. Inf. Theory, Whistler, British Columbia, p. 471, Sept. 1995.

....] 2. 1) where x t is the source symbol transmitted at time t and Y 1 0 is the received message (containing symbols) Starting with this definition of the final result required at the output of each decoder block, the BCJR algorithm can be modified to reduce its computational complexity [Pietrobon, 1995]. This simplifies its implementation in hardware and consequently improves the decoding speed. 1 Strictly, Turbo codes do not have an inner and outer code, because the concatenation used is parallel rather than serial. We use this notation, however, to denote the order of decoding in the ....

....though, that the parity bits in the tail region are transmitted for both encoders. The problem of terminating the parallel encoders in a Turbo code is that the interleaver causes the two trellises to finish in a different state, and hence different tail sequences are required. Barbulescu and Pietrobon [1995] propose a restriction on the interleaver pattern which forces the two trellises to end in the same state. This allows the use of a single tail sequence for both encoders. This type of interleaver is called a simile interleaver. 2.3.7 Interleaver Design While the effect of the interleaver on ....

[Article contains additional citation context not shown here]

PIETROBON, STEVEN SILVIO. 1995 (Sept.). Implementation and Performance of a Serial MAP Decoder for use in an Iterative Turbo Decoder. Page 471 of: Proceedings of the IEEE International Symposium on Information Theory.

....The UMP BP based decoding algorithm has been derived from the BP algorithm by considering only the dominant contribution when evaluating the reliability associated with each check sum. Therefore, the performance of this algorithm can be further enhanced by adding correction values, as described in [23] [25] for MAP based decoding algorithms. Furthermore, since for an (N; J; K) LDPC code, each check sum consists of K bits, with K small, this approach provides an alternative way to implement the BP algorithm as at most K Gamma 1 correcting values have to be added. This method becomes attractive ....

....sum consists of K bits, with K small, this approach provides an alternative way to implement the BP algorithm as at most K Gamma 1 correcting values have to be added. This method becomes attractive for hardware implementation of the BP algorithm since the corrective terms can be stored in a ROM [23] [25] Acknowledgement The authors wish to thank David J.C. MacKay for providing the generator matrices of the LDPC codes used in this paper by allowing access to his website, as well as the reviewers for improving the presentation of the paper. ....

S. S. Pietrobon, "Implementation and performance of a serial MAP decoder for use in an iterative turbo decoder," Proc. IEEE Int. Symp. Inform. Theory, Whistler, B.C., Canada, Sep. 1995, p. 471. 13

....When implemented in hardware, further modifications of the MAP algorithm can be used [28] Instead of working with probabilities, the logarithm of those probabilities was used to avoid overflow or underflow. This approach together with further simplifications is under current investigation [36]. The performance of both algorithms for the standard rate half four state systematic convolutional code (g 1 = 7 8 , g 2 = 5 8 ) is given in Table 2.1. The BER values are almost the same for an E b N 0 in the range 0 dB to 5 dB. The simulations were performed for at least 1500 errors in each ....

....concatenated coding schemes in order to approach channel capacity with lower complexity than maximum likelihood decoding algorithms. A simplified MAP algorithm was presented in Chapter 2. This algorithm has only four times the complexity of the Viterbi algorithm and can be implemented in hardware [36]. It is a maximum likelihood decoding algorithm which minimises the probability of bit error and provides soft outputs. Comparisons with other implementations were made in order to emphasise the reduction in computations which can be achieved. We also noted the higher dynamic range of its outputs ....

S. S. Pietrobon, "Implementation and performance of a serial MAP decoder for use in an iterative turbo decoder," to appear at the 1995 IEEE Int. Symp. Inform. Theory, Whistler, Canada, Sep. 1995.

....the complexity at the cost of the linear dependence on the number of decoding iterations. To achieve best performance, however, these decoders usually require maximum a posteriori (MAP) algorithm [1] which is of relatively high complexity if implemented straightforwardly. Modified MAP algorithms [2,27,30] and soft output Viterbi algorithm (SOVA) 18, 19] have thus been proposed in place of MAP decoders to reduce system complexity. Alternative high performance coding systems of low complexity are proposed in this paper via the generalized concatenation of convolutional codes. Of central focus is ....

S. S. Pietrobon, "Implementation and Performance of a Serial MAP Decoder for Use in an Iterative Turbo Dedoder," Proceedings of IEEE International Symposium on Information Theory '95, Whistler, BC, Canada, p. 471, Sept. 1995.

....data rates, decoding must be done in pipeline. The total delay would then be equal to D P # 2N i (D D # D I ) 6) where N i is the number of iterations and D D is the decoder delay. The decoder delay can be significantly reduced to a few hundred bits by using a continuous decoding algorithm [4, 11, 22]. 16 As can be seen from the above equation, the total bit delay can be quite large. However, since the data rate is high, the corresponding time delay can be made very small. 6 Examples of turbo decoders The first commercially available turbo decoder chip was produced in association with the ....

Pietrobon, S. S., "Implementation and performance of a serial MAP decoder for use in an iterative turbo decoder," 1995 IEEE Int. Symp. Inform. Theory, Whistler, Canada, pp. 471, Sep. 1995.

....to be greatly simplified so that it can be implemented in hardware with good performance in terms of speed and memory use. Particularly, complex operations like floating divisions and multiplications, exponentials and logarithms have to be avoided. We present here a modified algorithm derived in [9] which allows a hardware implementation to be made. 2 .2 .8 .1 Analysis of the MAP algorithm For each processed bit, the MAP decoder has to compute the # k function which requires one logarithm, one float division and 2(2 # # 1) float additions. Each term of the additions requires 2 float ....

....should also take into account that most of the CPU time was spent in computing the S f and S b functions. These functions can be incorporated into look up tables to greatly speed up the decoding time. 2 .2 .8 . 2 Improvement of the MAP algorithm All the results we develop here are derived from [9]. We have shown that the algorithm is efficient in our simulations. A software implementation has been produced, using the C programming language which is presented in Appendix 2. We define the E function as x E y = ln ( e #x # e #y ) Using the E function, we can now express the ....

[Article contains additional citation context not shown here]

S. S. Pietrobon, "Implementation and performance of a serial MAP decoder for use in an iterative turbo decoder," IEEE Int. Symp. Inform. Theory, Whistler, Canada, Sep. 1995. 78

....decoding algorithm [2] is used to decode each of the two (or more) individual parallel encoders in the turbo encoder. By converting the MAP algorithm from the probability domain to the logarithm domain [3,4] the algorithm can be further simplified so that it can be easily implemented in hardware [5,6]. Whatever the implementation though, the basic MAP algorithm suffers from having to decode data in large block sizes. This leads to large memory requirements and a large decoding delay. There is also the need to synchronise to the block, but this is necessary anyway in a turbo decoder. A small ....

....perform a read, followed by a write. Since the RAM address is inverted every N DCLK cycles, the old forward SM s are read out in reverse order. A control signal to the CE input of the RAM is used to enable the storage of the new SMs at the correct time. The above technique was successfully used in [5]. The same technique was also used for storing the BMs that were Q 0 # Q 15 Q 16 DCLK Depth Counter 16 CLK State Counter CP CP Q 0 # Q 3 16 20 4 WE CE CLK CTL CLK CP D Q 8 8 New SM A 0 # A 19 Din Dout CLK LE D Q 8 8 Figure 1: State Metric storage for block MAP decoder. CLK = clock CTL = control ....

S. S. Pietrobon, "Implementation and performance of a serial MAP decoder for use in an iterative turbo decoder," IEEE Int. Symp. Inform. Theory, Whistler, British Columbia, Canada, p. 471, Sep. 1995.

....SC) when the information bits are directly written to the output. When this is not the case, the code is a non systematic code. In the family of SC codes, the recursive codes are of particular interest because they perform better than non systematic codes at low signal to noise ratio [5]. 3.2. The trellis The trellis is very important in describing the MAP algorithm. It graphically depicts two features of an encoder transition from one state to another. These are the information bit which produced the transition and the corresponding next state of the transition. Let us consider ....

....sequences are thus totally decorrelated and MAP decoding should lead to good performance. However, in the receiver, we will first decode one of the two codes (usually G 1,1 G 1,0 ) The log likelihood ratio (LLR) for the information bits will be sent into the second MAP decoder. Reference [5] shows that the LLR function produces fairly correlated values in the range of a few tens of symbols. If we were to input this LLR directly into the second MAP decoder, the second MAP decoder output could produce even more erroneous data. To avoid this problem, the solution that has been chosen is ....

[Article contains additional citation context not shown here]

S. S. Pietrobon, "Implementation and performance of a serial MAP decoder for use in an iterative turbo decoder," IEEE Int. Symp. Inform. Theory, Whistler, British Columbia, Canada, p. 471, Sep. 1995.

No context found.

S. Pietrobon, "Implementation and Performance of a Serial MAP Decoder for use in an Iterative Turbo Decoder", Int. Symp. on Inform. Theory and its Applications, Sidney, NSW, Nov. 1994, pp. 1073-1077.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC