47 research outputs found
Approximate Linear Time ML Decoding on Tail-Biting Trellises in Two Rounds
A linear time approximate maximum likelihood decoding algorithm on
tail-biting trellises is prsented, that requires exactly two rounds on the
trellis. This is an adaptation of an algorithm proposed earlier with the
advantage that it reduces the time complexity from O(mlogm) to O(m) where m is
the number of nodes in the tail-biting trellis. A necessary condition for the
output of the algorithm to differ from the output of the ideal ML decoder is
reduced and simulation results on an AWGN channel using tail-biting rrellises
for two rate 1/2 convoluational codes with memory 4 and 6 respectively are
reporte
On the Minimum Distance of Generalized Spatially Coupled LDPC Codes
Families of generalized spatially-coupled low-density parity-check (GSC-LDPC)
code ensembles can be formed by terminating protograph-based generalized LDPC
convolutional (GLDPCC) codes. It has previously been shown that ensembles of
GSC-LDPC codes constructed from a protograph have better iterative decoding
thresholds than their block code counterparts, and that, for large termination
lengths, their thresholds coincide with the maximum a-posteriori (MAP) decoding
threshold of the underlying generalized LDPC block code ensemble. Here we show
that, in addition to their excellent iterative decoding thresholds, ensembles
of GSC-LDPC codes are asymptotically good and have large minimum distance
growth rates.Comment: Submitted to the IEEE International Symposium on Information Theory
201
Exact Free Distance and Trapping Set Growth Rates for LDPC Convolutional Codes
Ensembles of (J,K)-regular low-density parity-check convolutional (LDPCC)
codes are known to be asymptotically good, in the sense that the minimum free
distance grows linearly with the constraint length. In this paper, we use a
protograph-based analysis of terminated LDPCC codes to obtain an upper bound on
the free distance growth rate of ensembles of periodically time-varying LDPCC
codes. This bound is compared to a lower bound and evaluated numerically. It is
found that, for a sufficiently large period, the bounds coincide. This approach
is then extended to obtain bounds on the trapping set numbers, which define the
size of the smallest, non-empty trapping sets, for these asymptotically good,
periodically time-varying LDPCC code ensembles.Comment: To be presented at the 2011 IEEE International Symposium on
Information Theor
High-Rate Convolutional Codes with CRC-Aided List Decoding for Short Blocklengths
Recently, rate- zero-terminated and tail-biting convolutional codes
(ZTCCs and TBCCs) with cyclic-redundancy-check (CRC)-aided list decoding have
been shown to closely approach the random-coding union (RCU) bound for short
blocklengths. This paper designs CRCs for rate- CCs with
short blocklengths, considering both the ZT and TB cases. The CRC design seeks
to optimize the frame error rate (FER) performance of the code resulting from
the concatenation of the CRC and the CC. Utilization of the dual trellis
proposed by Yamada \emph{et al.} lowers the complexity of CRC-aided serial list
Viterbi decoding (SLVD) of ZTCCs and TBCCs. CRC-aided SLVD of the TBCCs closely
approaches the RCU bound at a blocklength of .Comment: 6 pages; submitted to 2022 IEEE International Conference on
Communications (ICC 2022
Woven Graph Codes: Asymptotic Performances and Examples
Constructions of woven graph codes based on constituent block and
convolutional codes are studied. It is shown that within the random ensemble of
such codes based on -partite, -uniform hypergraphs, where depends
only on the code rate, there exist codes satisfying the Varshamov-Gilbert (VG)
and the Costello lower bound on the minimum distance and the free distance,
respectively. A connection between regular bipartite graphs and tailbiting
codes is shown. Some examples of woven graph codes are presented. Among them an
example of a rate woven graph code with
based on Heawood's bipartite graph and containing constituent rate
convolutional codes with overall constraint lengths is
given. An encoding procedure for woven graph codes with complexity proportional
to the number of constituent codes and their overall constraint length
is presented.Comment: Submitted to IEEE Trans. Inform. Theor
Reversed-Trellis Tail-Biting Convolutional Code (RT-TBCC) Decoder Architecture Design for LTE
Tail-biting convolutional codes (TBCC) have been extensively applied in communication systems. This method is implemented by replacing the fixed-tail with tail-biting data. This concept is needed to achieve an effective decoding computation. Unfortunately, it makes the decoding computation becomes more complex. Hence, several algorithms have been developed to overcome this issue in which most of them are implemented iteratively with uncertain number of iteration. In this paper, we propose a VLSI architecture to implement our proposed reversed-trellis TBCC (RT-TBCC) algorithm. This algorithm is designed by modifying direct-terminating maximum-likelihood (ML) decoding process to achieve better correction rate. The purpose is to offer an alternative solution for tail-biting convolutional code decoding process with less number of computation compared to the existing solution. The proposed architecture has been evaluated for LTE standard and it significantly reduces the computational time and resources compared to the existing direct-terminating ML decoder. For evaluations on functionality and Bit Error Rate (BER) analysis, several simulations, System-on-Chip (SoC) implementation and synthesis in FPGA are performed