Application of Extrinsic Information Transfer Charts to Anticipate Turbo Code Behavior

Application of Extrinsic Information Transfer Charts to Anticipate Turbo Code Behavior

Izabella Lokshina (SUNY Oneonta, USA)
DOI: 10.4018/978-1-4666-2154-1.ch007
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This paper examines turbo codes that are currently introduced in many international standards, including the UMTS standard for third generation personal communications and the ETSI DVB-T standard for Terrestrial Digital Video Broadcasting. The convergence properties of the iterative decoding process associated with a given turbo-coding scheme are estimated using the analysis technique based on so-called extrinsic information transfer (EXIT) chart. This approach provides a possibility to anticipate the bit error rate (BER) of a turbo code system using only the EXIT chart. It is shown that EXIT charts are powerful tools to analyze and optimize the convergence behavior of iterative systems utilizing the turbo principle. The idea is to consider the associated SISO stages as information processors that map input a priori LLR’s onto output extrinsic LLR’s, the information content being obviously assumed to increase from input to output, and introduce them to the design of turbo systems without the reliance on extensive simulation. Compared with the other methods for generating EXIT functions, the suggested approach provides insight into the iterative behavior of linear turbo systems with substantial reduction in numerical complexity.
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The Process Of Extrinsic Information Transfer

The process of extrinsic information transfer can be described with analysis of iterative turbo decoder. The block diagram of an iterative turbo decoder is shown in Figure 1, where each APP decoder corresponds to a constituent encoder and generates the corresponding extrinsic information 978-1-4666-2154-1.ch007.m01 for m=1,2, using the corresponding received sequences.

Figure 1.

Block diagram of turbo decoder with two constituent decoders


The interleavers are identical to the turbo encoder’s interleavers, and they are used to reorder the sequences so that the sequences at each decoder are properly aligned. The algorithm is iterated several times through the two decoders; each time the constituent decoder uses the currently calculated a posteriori probability as input.

The a posteriori probabilities produced by the first decoder are shown as (1),

(1) where:
is the a posteriori probability of the systematic bits, which are conditionally independently distributed. Direct use of (1) would lead to an accumulation of “old” extrinsic information by calculating:

As a result, the decoders are constrained to exchange extrinsic information only, which is achieved by subtracting the input values to the APP decoders from the output values as indicated in Figure 1.

The extrinsic information is a reliability measure of each constituent decoder’s estimate of the transmitted information symbols based on the corresponding received constituent parity sequence only. Since each constituent decoder uses the received systematic sequence directly, the extrinsic information allows the decoders to share information without biasing.

The effectiveness of this technique can be seen in Figure 2, which shows the performance of the original (37, 21, 65536) turbo code as a function of the decoder iterations. It is remarkable that the performance of the code with iterative decoding continues to improve with increasing number iterations, but frequently, after 6 iterations a sufficient convergence has already been reached.

Figure 2.

Performance of the (37, 21, 65536) Turbo Code as Function of Decoder Iterations


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