08-05-2012, 12:01 PM
A New Approach for FEC Decoding Based on the BP Algorithm in LTE and WiMAX System
A New Approach for FEC Decoding Based on the.pdf (Size: 378.02 KB / Downloads: 56)
Abstract
Many wireless communication systems such as IS-
54, enhanced data rates for the GSM evolution (EDGE), worldwide
interoperability for microwave access (WiMAX) and long
term evolution (LTE) have adopted low-density parity-check
(LDPC), tail-biting convolutional, and turbo codes as the forward
error correcting codes (FEC) scheme for data and overhead channels.
Therefore, many efficient algorithms have been proposed for
decoding these codes. However, the different decoding approaches
for these two families of codes usually lead to different hardware
architectures. Since these codes work side by side in these new
wireless systems, it is a good idea to introduce a universal
decoder to handle these two families of codes. The present
work exploits the parity-check matrix (H) representation of tailbiting
convolutional and turbo codes, thus enabling decoding
via a unified belief propagation (BP) algorithm. Indeed, the
BP algorithm provides a highly effective general methodology
for devising low-complexity iterative decoding algorithms for all
convolutional code classes as well as turbo codes. While a small
performance loss is observed when decoding turbo codes with
BP instead of MAP, this is offset by the lower complexity of the
BP algorithm and the inherent advantage of a unified decoding
architecture.
I. INTRODUCTION
Until recently, most known decoding algorithms for
convolutional codes were based on either algebraically
calculating the error pattern or on trellis graphical
representations such as in the MAP and Viterbi algorithms.
With the advent of turbo coding [1], a third decoding
principle has appeared: iterative decoding. Iterative decoding
was also introduced in Tanner’s pioneering work [2], which
is a general framework based on bipartite graphs for the
description of LDPC codes and their decoding via the belief
propagation (BP) algorithm.
In many respects, convolutional codes are similar to block
codes. For example, if we truncate the trellis by which
a convolutional code is represented, a block code whose
codewords correspond to all trellis paths to the truncation
depth is created. However, this truncation causes a problem
in error performance, since the last bits lack error protection.
The conventional solution to this problem is to encode a
fixed number of message blocks L followed by m additional
all-zero blocks, where m is the constraint length of the
convolutional code [4]. This method provides uniform
error protection for all information digits, but causes a rate
reduction for the block code as compared to the convolutional
code by the multiplicative factor L/(L+m). In the tail-biting
convolutional code, zero-tail bits are not needed and replaced
by payload bits resulting in no rate loss due to the tails.
Therefore, the spectral efficiency of the channel code is
improved.
Due to the advantages of the tail-biting method over the
zero-tail, it has been adopted as the FEC in addition to the
turbo code for data and overhead channels in many wireless
communications systems such as IS-54, EDGE, WiMAX and
LTE [5, 6, 7].
Both turbo and LDPC codes have been extensively studied
for more than fifteen years. However, the formal relationship
between these two classes of codes remained unclear until
Mackay in [8] claimed that turbo codes are LDPC codes.
Also, Wiberg in [9] marked another attempt to relate these
two classes of codes together by developing a unified factor
graph representation for these two families of codes. In [10],
McEliece showed that their decoding algorithms fall into
the same category as BP on the Bayesian belief network.
Finally, Colavolpe [11] was able to demonstrate the use of the
BP algorithm to decode convolutional and turbo codes. The
operation in [11] is limited to specific classes of convolutional
codes, such as convolutional self orthogonal codes (CSOCs).
Also, the turbo codes therein are based on the serial structure
while the parallel structure is more prevalent in practical
applications.
In LTE and WiMAX systems, the proposed decoders for
the tail-biting convolutional codes and turbo codes are based
on the Viterbi and MAP algorithms, respectively. However,
many other efficient algorithms have been proposed to decode
tail-biting convolutional codes as well as turbo codes. For
example, in [3], the reduced complexity wrap-around Viterbi
algorithm was proposed to decode tail-biting convolutional
codes in the WiMAX system to reduce the average number
of decoding iterations and memory usage. In addition,
other decoding algorithms such as double traceback and
bidirectional Viterbi algorithms were also proposed for
tail-biting convolutional codes in LTE [4]. Finally in [5], the
design and optimization of low-complexity high performance
rate-matching algorithms based on circular buffers for LTE
turbo codes was investigated.
In this paper, we focus on the direct application of the
BP algorithm used for LDPC codes to decode the tail-biting
convolutional codes and turbo codes in WiMAX and LTE
978-1-4577-0742-1/11/$26.00 ©2011 IEEE 9
systems, respectively. Based on that, we propose a decoder
with drastically lower implementation complexity than that
proposed in the latest releases for these systems [5-7].
The rest of this paper is organized as follows. In Section II
and III, the graphical representation of the tail-biting convolutional
and turbo codes with the necessary notations and definitions
used throughout this paper are introduced, followed by
an investigation of the coding structures in WiMAX and LTE
systems in Section IV. In Section V, simulation results for the
performance of tail-biting convolutional and turbo codes using
the proposed algorithm are introduced followed in Section VI
by a complexity comparison between the proposed algorithm
and the traditional ones. Finally, the paper is concluded in
Section VII.