Robust Decoding for Convolutionally Coded Systems Impaired by Memoryless Impulsive Noise

Abstract

It has been known that communication systems are susceptible to strong impulsive noises. To combat this, convolutional coding has long served as a cost-effective tool in the context of moderately frequent occurrence of memoryless impulses with given statistics. Nevertheless, the impulsive noise statistics is hard to be accurately modeled and is generally not time-invariant, making the respective system design challenging. In this article, in the absence of full knowledge of the probability density function (PDF) of impulsive noises, we devise an efficient decoding scheme for single-carrier narrowband communication systems by incorporating a design parameter into the recently introduced joint erasure marking and This is the Pre-Published Version 2 Viterbi decoding algorithm, dubbed the metric erasure Viterbi algorithm (MEVA). The proposed scheme is equivalent to incorporating a well-designed clipping operation into the Viterbi algorithm, of which the clipping threshold has to be appropriately set. In contrast with existing publications that often resort to extensive simulations, we characterize the bit error probability performance associated with the clipping threshold by deriving its Chernoff bound. Simulation results reveal that with a judicious selection of the clipping threshold, the MEVA can be on par with its optimal maximum-likelihood decoding counterpart under fairly general circumstances.

Optimized metric clipping decoder design for impulsive noise channels at high signal-to-noise ratios

“…The decoding decision is based on choosing x that maximizes the decoding metric m(t, r, x), where t is the clipping threshold of the Euclidean metric [11] which is to be optimized, x is the transmitted signal sequence, i.e., a codeword, r is the received signal samples at the output of the communication channel. Denoting byx the competing codeword, the metric difference of the two codewords can be expressed as…”

“…Thus, Δm(t, ri, xi,xi) can be expressed in terms of t and ni and for notational convenience, we define Δ(t, ni, xi,xi) = Δm(t, √ E + ni, xi,xi). The metric difference for each bit Δ(t, ni, xi,xi) under t ≥ √ E is given in [11] as,…”

“…However, a systematic way to choose the clipping threshold is unavailabe in [10]. In [11], by interpreting the Viterbi algorithm with a clipped Euclidean metric as a special form of JEVA that can mark a varying number of erasures, the so-called metric erasure Viterbi algorithm (MEVA) was proposed and a systematic way to choose the clipping threshold was derived by assuming the impulsive noise probability is close to 1. The aforementioned metric clipping based decoders are easy to implement as practical decoders always adopt some form of metric clipping due to the finite bit precision in digital circuit implementation.…”

“…The aforementioned metric clipping based decoders are easy to implement as practical decoders always adopt some form of metric clipping due to the finite bit precision in digital circuit implementation. However, the assumption made in [11] (and implicitly in [10]) about the noise statistics for deriving the clipping threshold are violated at high SNR which leads to an error floor in bit error probability curve, as shown in the Experimentsl Results Section.…”

“…The selection of the metric clipping threshold is formulated as an optimization problem without estimating the impulsive noise statistics. Compared with MEVA [11], our optimization problem is analytically formulated using the exact pairwise error provability (PEP), rather than choosing the parameter with the plots of Chernoff bounds. To evaluate the performance, simulations are conducted under the Bernoulli Gaussian model over a wide range of parameters.…”