Combined puncturing and path pruning for unequal error protection

Abstract

In -this paper, we propose a new class of the hybrid punctured and path-pruned convolu- tional codes by combining two conventional tech- niques for unequal error protection (UEP): punctur- ing and path pruning. The hybrid codes can provide flexible choices of code rate and powerful UEP ca- pabilities. By properly puncturing and pruning the parent code, decoding of the hybrid codes can also be done by a single decoder for the parent code. The rate-compatible punctured convolutional (RCPC) codes ( 11 and the path-compatible pruned convolutional (PCPC) codes (2) are two unequal error protection (UEP) schemes constructed by puncturing and path pruning ordinary convolutional codes, called parent codes, respectively. Both approaches provide good UEP performance but have many complementary properties in nature. For instance, compared with the parent code, RCPC codes are of higher code rates and poorer bit error rate (BER) performance, but PCPC codes have lower code rates and better BER performance. More- over, RCPC codes can provide flexible choices of code rate by tuning the puncturing period but suffer from large number of the long error events due to puncturing. PCPC codes, on the other hand, take the advantage of sparse distance spectra, but only few of code rates are available if the (n, IC) parent codes of small k are chosen. To gain the advantages of RCPC and PCPC codes, we combine puncturing and path pruning on convolutional codes and construct a new class of the hybrid punctured and path-pruned convolutional codes for UEP. Consider an (n, k) parent code C with generator matrix G(D). Suppose C is first pruned by a path locating matrix O(D) and then punctured by a puncturing matrix P with puncturing period M. The resulting hybrid code can be for- mulated as a subcode of C with generator matrix