Statistical Simulator for Block Coded Channels with Long Residual Interference

Abstract

Abstract-In this paper, we present a simple statistical simulation technique for channels with long memory operating under coded data. The proposed technique employs a divideand-conquer approach, both at the level of the channel response and the individual codeword. We introduce an efficient algorithm for parity tracking during the generation and combining of the voltage distributions computed in individual sub-problems. The resulting computational complexity increases linearly both with the channel and the codeword length, keeping the number of parity bits constant. The complexity increases exponentially with the number of parity bits in a codeword. Thus, the technique is of most use for high-rate codes. Finally, the technique is applied to examine the effect of coding on high-speed links which operate at BERs smaller than 1e-15 and where residual interference typically spans several hundreds of bits. This simulator enables systematic evaluation of power-performance trade-offs in introducing error correction/detection codes into high-speed link systems.

An electrical-level superposed-edge approach to statistical serial link simulation

“…Although beyond the scope of this paper, it is possible to extend the edge-based method to handle such features as decision-feedback equalization, 8b/10b and other types of encoding [8], as well as crosstalk from neighboring channels.…”

“…If the transmitted bits have not been encoded, then the individual bits are uncorrelated (the case of bit correlation due to encoding was considered in [8]). Assuming that bits are uncorrelated and that pulse responses can be superposed leads to a particularly simple formula for the PDF needed for bit-error rate estimation,…”

“…One use of the Γ notation is to simplify the description of the inductive approach for computing the probability density function needed for computing bit-error rates, f Vτ |B (v|b). Since f Vτ |B (v|b) = f V 0 τ |B 0 (v|b), and since the probability density function, f V N τ |B N (v|b) is known (see equation (8)), f Vτ |B (v|b) can be computed by starting with f V N τ |B N (v|b) and repeatedly applying Γ. That is, Γ can used to compute…”

Channel Coding For High-Speed Links: A Systematic Look at Code Performance and System Simulation

“…It follows that the underlying symbol constraints in a coded system likely have little direct effect on the marginal and joint error statistics prior to decoding. 8 However, more significant inaccuracies may arise from the error behavior at the boundaries between blocks, as at least one symbol in each block is affected by the ISI from the preceding blocks. The quality of this approximation for a given codeword length improves with a decreasing number of blocks, which yields a direct method of trading off computing speed for accuracy.…”

“…Due to constraints on the symbol stream, the marginal error probabilities are no longer equal across different symbols. An efficient method of computing for different symbol locations in a codeword is described in [8], which focuses on systematic binary linear block codes. However, the performance of a coded system cannot be expressed through marginal error statistics alone, but is instead dependent on the joint error behavior.…”