Designing a non-catastrophic puncturing mask with punctured data bits [15] is an easy task for the first (non-interleaved) constituent CRSC code of the TC. For in-stance, it can be performed by a modified FAST algorithm. However, when design-ing TC interleavers, these techniques do not guarantee a good correspondence of the puncturing pattern with respect to the second (interleaved) constituent CRSC code.
To deal with this issue, data puncturing constraints must be taken into consideration when designing the interleaver.
As far as we know, no puncturing constraint related to parity puncturing has been included in the design of TC interleavers so far. The analysis carried out in this work allows to identify a useful parity puncturing constraint for the design of TC interleavers. The state-of-the-art data puncturing constraints and the proposed parity puncturing constraint are described in the following sections.
2.3.1 State-of-the-art data puncture-constrained interleavers for TCs
Let us consider a TC interleaver structure as described in Section 1.2. A Data Puncture-Constrained (DPC) interleaver ensures that for a given puncturing pattern the data punctured positions in the data sequence d are interleaved to data punc-tured positions in the interleaved data sequenced0. Two types of DPC interleavers have been proposed in the literature: fully-constrained and partially-constrained interleavers.
2.3. PUNCTURING CONSTRAINTS 39 In fully-constrained interleavers [12], [80], symbols at positionn,n = 0, ..., N−1, within a puncturing pattern with period N in d are interleaved to the same posi-tion n within a puncturing pattern in d0. This ensures the same puncturing mask in both constituent CRSC codes, avoiding poor puncturing patterns. In partially-constrained interleavers, data punctured positions indare interleaved to data punc-tured positions in d0. This interleaver structure allows two different puncturing masks to be used for the constituent codes, provided that the number of data punc-tured positions in both masks remains the same. Then, partially-constrained inter-leavers have a more flexible structure than fully-constrained interinter-leavers. Indeed, a larger number of partially-constrained interleavers can be found validating other design criteria (e.g., span and correlation girth) than fully-constrained. Therefore, TC interleavers proposed in this study are partially-constrained.
2.3.2 Proposed parity puncturing constraint
During the turbo decoding process, extrinsic information from a given constituent decoder is generated based on its received parity sequence and is sent to the other constituent decoder via the interleaver/deinterleaver asa priori information on data.
The extrinsic information computed from unpunctured parity positions is expected to be more reliable than the one generated from punctured parity positions. There-fore, an analysis of the connection strategy applied by the interleaver for unpunc-tured parity positions of a constituent code, and the effect of the information ex-change on the remaining code, are of relevance for performance improvement. The proposed connection strategy defines a new puncturing constraint related to parity puncturing. Thus, an interleaver including both data and proposed parity punctur-ing constraint is named Data and Parity Puncture-Constrained (DPPC) interleaver.
2.3.2.1 Extrinsic information analysis
In order to illustrate the reliability difference between extrinsic information evalu-ated from punctured and unpunctured parity positions, a conventional EXIT chart, as introduced in Section 1.1.1.4, was calculated for a parity-only punctured version of a TC with a uniform interleaver. As shown in Fig. 2.1, the EXIT curve obtained from data at unpunctured parity positions has a more opened tunnel than the one obtained from data at punctured parity positions. These results validate thea priori assumption that extrinsic information computed from unpunctured parity positions is more reliable than the one generated from punctured parity positions.
2.3.2.2 Connection strategy for the unpunctured parity positions
Since extrinsic information corresponds toa priori information on data, a possible strategy for the interleaver construction involves connecting the most reliable
ex-40 CHAPTER 2. EFFICIENT PUNCTURE-CONSTRAINED INTERLEAVER
0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0
Complete frame
Unpunctured parities
Punctured parities
IE1,IA2
IA1, IE2
Figure 2.1: Comparison of EXIT charts computed from the complete data frame and from punctured and unpunctured parity positions at the SNR decoding threshold over the AWGN channel.
trinsic information positions from one constituent decoder to the most error-prone data positions in the other one. Under these conditions, the turbo decoding decision on the most error-prone data positions should be improved. For a given punctur-ing mask with period N and data puncturing rate DPR, the proposed connection strategy is defined by the following steps:
1. Identify the number of free parities within a puncturing period N: Free paritiesare defined as unpunctured parities corresponding to unpunctured data symbols.
2. Identify error-prone data positions within a puncturing period N: To this end, additional data puncturing is introduced at the remaining unpunc-tured data positions, and the resulting CRSC distance spectrum is evaluated.
The number of additional punctured data positions corresponds to the num-ber of free parities. The additional punctured data positions leading to the poorest CRSC distance spectrum are then labeled as the most error-prone. It is noteworthy that additional data puncturing is only introduced to identify error-prone data positions. These additional punctured data positions are removed from the puncturing mask after the corresponding identification.
3. Apply the connection strategy: The proposed strategyinvolves connecting free parities of a CRSC code to the most error-prone data positions of the other one. Thus, in the decoder, the most reliable extrinsic information positions
2.4. NEW REPRESENTATION OF THE CORRELATION GRAPH FOR TCS41