Staircase Codes for High-Rate Wireless Transmission on Burst-Error Channels

Variable‐rate staircase codes with RS component codes for optical wireless transmission

“…C.ah C de fc bg/sz 2 C.ad bc/z 2 C .eh fg/s 2 z 2 (27) To find the initial conditions, let H P .s, z/ D a 0 C a 1 z C a 2 sz C a 3 sz 2 : : :, and multiply both sides of Equation (27) by its denominator, then equate the coefficients of each indeterminates s, z. As we will allow for a negative index in the recurrence relation, the condition P.m, n/ D 0 for m, n < 0 must hold, and only a 0 , a 1 and a 2 are required for the initial conditions [26] as a 3 , a 4 , : : : can be obtained from the recursion.…”

“…It can be seen that the curves of rate-adaptive staircase codes coincide with the upper bound of the RS assist codes at high input bit error probability, the actual waterfall region occurs at a lower input bit error probability than the analysis curves, because the iterative decoding threshold gives the bound for unsuccessful iterative decoding, above which the iterative decoding will definitely fail; thus below the iterative decoding threshold, the iterative decoding is a possible success. Figure 8 depicts performance of rate-adaptive staircase codes on a burst-error channel using Gilbert-Elliot model parameter set up as in [27] with average burst length of 10. We observe that the baseline staircase BCH code can correct fewer errors than on the random-error channel, so it can only correct for an input bit error probability of almost p E D 0.0014 with an output bit error probability of p O D 10 6 .…”

Staircase construction with non-systematic polar codes

“…Staircase codes are a powerful product-like code construction first proposed in [1], an incarnation of which is standardized in the ITU-T G.709.2 recommendation for optical transport networks [2], in the OIF 400-ZR implementation agreement for 400Gb/s coherent links [3]; they have also been considered for wireless transmission [4]. They can be viewed as spatially-coupled codes with a specific interleaver shape; they introduce a memory element and are usually based on systematic algebraic codes [5].…”