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<CENTER><B><FONT size=+1>Linear Block Codes: Performance analysis
tools</FONT></B></CENTER>
<P>Here are several programs written in C and Matlab scripts for the analysis
and simulation of various linear block codes over BSC, AWGN and Rayleigh
fading channels. This is the topic of Chapter 1 of the <A
href="http://www.amazon.com/gp/product/0470015586/ref=sr_11_1/102-3025380-7157754?ie=UTF8">book</A>.
<BR></P>In addition to the programs below, the following two directories
contain, respectively, the <SPAN style="FONT-WEIGHT: bold">generator matrices
and weight distributions of all binary extended BCH codes of length up to
128</SPAN>: <BR><A
href="http://the-art-of-ecc.com/Matrices_BCH">Matrices_BCH</A> <BR><A
href="http://the-art-of-ecc.com/Weights">Weights_BCH</A> <BR><BR><SPAN
style="FONT-WEIGHT: bold">Simulation of BPSK modulation over an AWGN
channel:</SPAN><BR><A
href="http://the-art-of-ecc.com/1_Linear/sim_bpsk.m">sim_bpsk.m</A> which also
needs <A href="http://the-art-of-ecc.com/1_Linear/Q.m">Q.m</A><BR><BR><SPAN
style="FONT-WEIGHT: bold">Use of the Hamming bound to determine minimum
redundancy n-k, given k and t:</SPAN><BR><A
href="http://the-art-of-ecc.com/1_Linear/minred.m">minred.m</A><BR><BR><SPAN
style="FONT-WEIGHT: bold">Use of the Hamming bound to determine maximum t, given
k and redundancy n-k:</SPAN><BR><A
href="http://the-art-of-ecc.com/1_Linear/maxt.m">maxt.m</A><BR>
<P><B>Simulation of a (6,3,3) linear code, over BSC, AWGN and Rayleigh fading
channels:</B> <BR><A
href="http://the-art-of-ecc.com/1_Linear/633_awgn.c">633_awgn.c</A> <BR><A
href="http://the-art-of-ecc.com/1_Linear/633_awgn_hdd.c">633_awgn_hdd.c</A>
<BR><A
href="http://the-art-of-ecc.com/1_Linear/633_rayleigh.c">633_rayleigh.c</A>
<BR></P>
<P><B>Weight distribution of a linear code given its generator matrix in an
input file:</B> <BR><A
href="http://the-art-of-ecc.com/1_Linear/WD_linear_code.c">WD_linear_code.c</A>
</P>An example is the binary linear (6,3,3) code discussed in the book, for
which the file should contain the following 3 lines: <BR>100110 <BR>010011
<BR>001101 <BR><BR><SPAN style="FONT-WEIGHT: bold">Compute the weight
distribution and union bound of a binary linear code and union bound for binary
transmission over an AWGN channel:</SPAN><BR><A
href="http://the-art-of-ecc.com/1_Linear/WeightDistribution.m">WeightDistribution.m</A><BR>
<P><B>Another C program to find the weight distribution of a binary linear code
given a generator matrix (better user interface, no prompt):</B> <BR><A
href="http://the-art-of-ecc.com/1_Linear/find_weights.c">find_weights.c</A>
</P>
<P><B>Bounds on the probability of a block error (WER) and a bit error (BER) for
binary linear codes with binary transmission over a Rayleigh fading channel:</B>
<BR><A
href="http://the-art-of-ecc.com/1_Linear/WER_Chernoff.c">WER_Chernoff.c</A>
<BR><A
href="http://the-art-of-ecc.com/1_Linear/WER_MC_union.c">WER_MC_union.c</A>
<BR><A
href="http://the-art-of-ecc.com/1_Linear/BER_Chernoff.c">BER_Chernoff.c</A>
<BR><A
href="http://the-art-of-ecc.com/1_Linear/BER_MC_union.c">BER_MC_union.c</A>
<BR></P>
<P><B>Union bound on the word error probability (WER) for a binary linear
block code over a BSC channel:</B> <BR><A
href="http://the-art-of-ecc.com/1_Linear/bound_pe.c">bound_pe.c</A> <BR></P>
<P><B>Bounds on the probability of a bit error for a linear code with
soft-decision and hard-decision decoding with binary transmission over an AWGN
channel:</B> <BR><A
href="http://the-art-of-ecc.com/1_Linear/bound_awgn_ebno.c">bound_awgn_ebno.c</A>
<BR><A
href="http://the-art-of-ecc.com/1_Linear/bound_hdd_awgn.c">bound_hdd_awgn.c</A>
<BR></P>
<P><B>Bounds on the bit error probability of the memory-2 rate-1/2 convolutional
code discussed in the book:</B> <BR><A
href="http://the-art-of-ecc.com/1_Linear/bound_rate12_bsc.c">bound_rate12_bsc.c</A>
<BR><A
href="http://the-art-of-ecc.com/1_Linear/bound_rate12_bsc_best.c">bound_rate12_bsc_best.c</A>
<BR><A
href="http://the-art-of-ecc.com/1_Linear/bound_rate12_bsc_meeberg.c">bound_rate12_bsc_meeberg.c</A>
</P>
<P><B>Evaluation of the undetected error probability of a binary linear (4,2,2)
code, Equation (1.27) in the book:</B> <BR><A
href="http://the-art-of-ecc.com/1_Linear/bound_undetect_422.c">bound_undetect_422.c</A> </P>
<P><B>Bounds on the probability of error of a repetition code over an AWGN
channel and a Rayleigh fading channel, with soft decision decoding, as well as
probability of error with hard-decision over an AWGN channel:</B> <BR><A
href="http://the-art-of-ecc.com/1_Linear/bound_313.c">bound_313.c</A> <BR><A
href="http://the-art-of-ecc.com/1_Linear/pe313_rayleigh.c">pe313_rayleigh.c</A>
<BR><A
href="http://the-art-of-ecc.com/1_Linear/pe_313_hd_awgn.c">pe_313_hd_awgn.c</A>
<BR></P>
<P><B>Simulation of a repetition (3,1,3) code over a binary symmetric
channel:</B> <BR><A
href="http://the-art-of-ecc.com/1_Linear/simulation313.c">simulation313.c</A>
<BR></P><SPAN style="FONT-WEIGHT: bold">Decoding of the binary (3,1,3) code over
an AWGN channel:</SPAN><BR><A
href="http://the-art-of-ecc.com/1_Linear/MLdecoder_313code.m">MLdecoder_313code.m</A><BR><BR><SPAN
style="FONT-WEIGHT: bold">Decoding of a binary (4,2,2) code over an AWGN
channel:</SPAN><BR><A
href="http://the-art-of-ecc.com/1_Linear/MLdecoder_422code.m">MLdecoder_422code.m</A><BR>
<P><B>Probability of decoding error (block error) for a binary code with binary
transmission over an AWGN channel and hard-decision decoding:</B> <BR><A
href="http://the-art-of-ecc.com/1_Linear/pe_hdd_awgn.c">pe_hdd_awgn.c</A>
<BR></P>
<P><B>Exact probability of error with standard array decoding of binary linear
codes:</B> <BR><A
href="http://the-art-of-ecc.com/1_Linear/pe_std_array.c">pe_std_array.c</A>
<BR></P>
<P><B>Evaluate error probabilities for an RS code:</B> <BR><A
href="http://the-art-of-ecc.com/1_Linear/prob_error_RScode.c">prob_error_RScode.c</A>
<BR><A
href="http://the-art-of-ecc.com/1_Linear/prob_dec_error_rs.c">prob_dec_error_rs.c</A>
<BR> </P>
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<H6 style="FONT-WEIGHT: normal"><FONT color=#000000>This page was last updated
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