Bounded-Metric List Decoding of Linearly Expurgated Tail-Biting Convolutional Codes

In the short blocklength regime, serial list decoding of tail-biting (TB) convolutional codes concatenated with an expurgating linear function (ELF) can approach the random coding union bound on frame error rate (FER) performance. Decoding complexity for a particular received word depends on how deep in the list the decoder must search to find a valid TB-ELF codeword. The average list size is close to one at low-FER operating points such as 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−6</sup>, and serial list decoding provides a favorable average complexity compared to other decoders with similar performance for these cases.However, the average list size can be on the order of a hundred or a thousand at higher, but still practically important, FER operating points such as 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup>. It is useful to study the tradeoff between how deep the decoder is willing to search and the proximity to the frame error rate (FER) achieved by an ML decoder. Often, this tradeoff is framed in terms of a maximum list depth. However, this paper frames the tradeoff in terms of a maximum allowable metric between the received word and the trellis paths on the list. We consider metrics of Euclidean distance and angle.This new approach draws on the wealth of existing literature on bounded-metric decoding to provide characterizations of how the choice of maximum allowable metric controls the tradeoffs between FER performance and both decoding complexity and undetected error rate. These characterizations lead to an example of an ELF-TB convolutional code that outperforms recent results for polar codes in terms of the lowest SNR that simultaneously achieves both a total error rate less than $\varepsilon _ \top ^{\ast} = {10^{ - 3}}$ and an undetected error rate below $\varepsilon _{\text{U}}^{\ast} = {10^{ - 5}}$.