A Discrete Time Markov Chain Model for High Throughput Bidirectional Fano Decoders

Abstract

Abstract-The bidirectional Fano algorithm (BFA) can achieve at least two times decoding throughput compared to the conventional unidirectional Fano algorithm (UFA). In this paper, bidirectional Fano decoding is examined from the queuing theory perspective. A Discrete Time Markov Chain (DTMC) is employed to model the BFA decoder with a finite input buffer. The relationship between the input data rate, the input buffer size and the clock speed of the BFA decoder is established. The DTMC based modelling can be used in designing a high throughput parallel BFA decoding system. It is shown that there is a tradeoff between the number of BFA decoders and the input buffer size, and an optimal input buffer size can be chosen to minimize the hardware complexity for a target decoding throughput in designing a high throughput parallel BFA decoding system. Index Terms-Bidirectional Fano algorithm, high throughput decoding, queuing theory, sequential decoding.

Low-complexity high-throughput decoding architecture for convolutional codes

“…A single UFA/BFA decoder with a finite input buffer can be treated as a D/G/1/B queue [21], in which D means that the input data rate is deterministic, G means that the decoding time is generic, 1 means that there is one decoder and B is the number of codewords the input buffer can hold. The state of the Fano decoder is represented by the input buffer occupancy or queue length when a codeword just finishes decoding, which is measured in terms of branches or information bits stored in the buffer.…”

“…The accuracy of the model degrades as B gets smaller. However, a very short input buffer will not be adopted according to the trade-off between area and decoding throughput as discussed in [21]. Additionally, it has also been found that the accuracy of the model does not depend on the relationship between M and N (i.e., M >N, M = N or M <N) as long as the input buffer size is large enough.…”