Analysis and design of punctured rate-1/2 turbo codes exhibiting low error floors

Abstract

Abstract-The objective of this paper is two-fold. Initially, we present an analytic technique to rapidly evaluate an approximation to the union bound on the bit error probability of turbo codes. This technique exploits the most significant terms of the union bound, which can be calculated straightforwardly by considering the properties of the constituent convolutional encoders. Subsequently, we use the bound approximation to demonstrate that specific punctured rate-1/2 turbo codes can achieve a lower error floor than that of their rate-1/3 parent codes. In particular, we propose pseudo-random puncturing as a means of improving the bandwidth efficiency of a turbo code and simultaneously lowering its error floor.

On the design of PS-RCPT codes for LTE system

“…It can be predicted by the union bound estimate from the weight spectrum of the 1/2-code rate RCPT codes that, all PS-RCPT codes can obtain a lower error floor than the 1/3-code rate mother code within the high SNR region. The PRP-RCPT code with 66% systematic bit puncturing ratio (we consider this ratio since its distance spectrum is better than the PRP-RCPT code with 57.1%, as illustrated in Table 1) can achieve better error floor performance than the S-RCPT code, which complies with [8]. However, it can be observed that the performance of PRP-RCPT codes is obviously inferior to the OWSS-criterion based optimized PS-RCPT codes.…”

“…The code rates of all RCPT codes in Table 1 are fixed as 1/2, and influence of the systematic bit puncturing ratio N s /P (marked with "Ratio" in Table 1) is also presented. It can be seen that the OWSS criterion based PS-RCPT codes with sufficiently large information puncturing ratio (in this example, N s /P ≥ 25% ) have larger free distance than the PRP-RCPT codes with systematic bit puncturing ratio 57.1% and 66% (only these two systematic bit puncturing ratios are included here since only they are reported in [8]), which implies that the optimized OWSS criterion based PS-RCPT codes can achieve a lower error floor. Meanwhile, it can be observed that a larger information puncturing ratio is desirable for the PS-RCPT codes to realize a lower error floor performance.…”

“…7 Compute the least L terms in Z for all candidates {Ã(r)}. 8 Determine the optimal one from all candidates according to the OWSS criterion. Update A(r) with the selected candidate.…”

“…However, it must be addressed that, all these previous works only considered the systematic RCPT (S-RCPT) code design (namely, no systematic bits are allowed to be punctured). Recently, it has been foound that, by allowing some systematic bits to be perforated, the partially systematic RCPT (PS-RCPT) codes with code rate 1/2 can achieve even better reliability than the 1/3 code rate mother codes, and the pseudo-random puncturing (PRP) scheme was proposed to devise the 1/2-rate PRP-PS-RCPT codes in [8].…”

Efficient Parallel Search Algorithm for Determining Optimal R=1/2 Systematic Convolutional Self-Doubly Orthogonal Codes

“…The first set comprises the two Maximum Free Distance (MFD) nonsystematic Viterbi codes (K = 7 and K = 9). The second set comprises the simulated floor regions of two modern punctured rate-1/2 Turbo codes [24] employing an interleaver size of 1000 bits, and after 8 decoding iterations. The specific codes used were a pseudo-randomly punctured Turbo code (PRP-PCCC) and a punctured systematic Turbo code (S-PCCC), both having a rate-1/3 PCCC(1,5/7,5/7) parent code.…”