Questions tagged [channelcoding]

Questions related to channel coding, forward error correction, code performance calculations, and decoding algorithms. Typical code examples are Hamming codes, cyclic codes, BCH, Reed-Solomon, turbo codes, and LDPC.

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Bose Chaudhuri Hocquenghem (BCH) vs Reed Solomon (RS) Error correcting codes and sound transmission channel modeling

I've implemented an acoustic based information transmission system using a bandwidth of 2 kHz and the band between 18.5 and 20.5 kHz. I'm trying to find the best error correcting code for it, in the ...
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1answer
302 views

Source and channel encoding

In information theory, there are two concepts that are widely used: source encoding and channel encoding. I'm afraid I may not be capable of expressing my doubts clearly, but the thing is that I don'...
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191 views

Mechanics of a matrix Interleaver

I am having trouble understanding exactly how the matrix interleaver. I have read the following page from MathWorks. In it, it gives the following example where "123456" is interleaved as "142536." ...
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What is the theoretical probability of error for OOK transmission?

I am trying to simulate an optical wireless communication channel which uses OOK modulation. Looking at equation 14 in this literature, I found that: For electrical SNR at the receiver $$\textrm{...
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1answer
146 views

Fountain codes and LDPC codes

I am having a small clarification with the difference between LDPC and fountain codes. In LDPC codes, each parity bit is depenedent on numerous data bits. Isn't that similar to fountain codes as the ...
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1answer
214 views

Finding $E_b/N_0$ when coding rate is $R_c$

I would like to calculate $E_b/N_0$ when the code rate is $R_c$ for BPSK signal. What I got this $$ E_b/N_0= \frac{1}{2R_mR_c \sigma^2} $$ and that is the case also according to this page. $R_m=1$ ...
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563 views

Relationship between $E_b/N_0$ and $\rm SNR$ with channel coding

I would like to know what would be the relationship between $E_b/N_0$ and $\rm SNR$ when there is a coding rate of $R_c=K/N$. Normally when there is no channel coding according to this link. $$\...
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1answer
124 views

Adding AWGN noise with certain power

Assume I have a signal(BPSK) and it has a certain amplitude. I would like to add a noise with a certain power to it. Assume I am using coding rate Rc as well. One method I am thinking would be to ...
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60 views

Difference between sticky channel Poisson-repeat channel

I don't quite understand the difference between a sticky channel and Poisson-repeat channel. A sticky channel allows duplications of symbols sent over the channel, then the block structure at the ...
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1answer
208 views

Relationship between information retrieval and source separation in signal processing

In machine learning, for the task of classifying input data (called an example) which are in binary representation, $\mathbf{x}\in \mathbb{R}^D$, $\mathbf{x} \in \{0,1\}^D$ into its multiple class ...
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48 views

Do convolution encoders exist with two separate (independent) inputs?

Do convolution encoders exist with two separate (independent) inputs? I got the question in my mind when I saw the question attached here.
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167 views

Code rate in IEEE 802.11b (DSSS)

I would like to know what code rates for forward error correction the physical layer of IEEE 802.11b uses for the different supported data rates. So far I didn't find any source for that. Actually in ...
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1answer
658 views

Golay complementary sequences in 802.11ad

The Golay complementary sequences consist of two sequences of the same length $N$ such that there acyclic autocorrelation sequences have sidelobes equal in magnitude but opposite in sign. So, when the ...
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621 views

Generating LDPC codes of arbitrary sizes in MATLAB

I am having problems generating LDPC codes of arbitrary sizes in MATLAB primarily because MATLAB insists on the parity check matrix that is input into its ldpcenc ...
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1answer
362 views

What is the cost of Hamming coding?

We know that (7,4) hamming code has 4 message bits and 7 code bits and can detect any single bit error. The (12,4) repetition code has 4 message bits and 12 code bits and can detect any single bit ...
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35 views

What is special about the theorem that over GF(2), $f^2(X) = f(X^2)$?

What is special about the theorem that over GF(2), $f^2(X) = f(X^2)$? There is a some 10-line proof for the same in "page no.42, Shu Lin, Daniel J. Costello-Error Control Coding (2nd Edition)-...
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222 views

Why is $x$ not considered a primitive polynomial while being considered an irreducible polynomial?

In "Shu Lin, Daniel J. Costello-Error Control Coding (2nd Edition), Prentice Hall 2004" it is given that in $GF(2)$, if $f(x)$ is an irreducible polynomial of degree $m$ it divides $x^n+1$ where $n = ...
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136 views

How to write cyclic codes?

I am studying cyclic codes. From what I understood of it, a cyclic code is a special kind of linear code with the property that any codeword cyclic shift is also a codeword. Generally, we start with ...
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46 views

In cyclic codes, a code vector can be obtained from another by simple circular shift. Why then the other method?

In cyclic codes, a code vector can be obtained from another by simple circular shift. Why then the other method is taught that is a bit round about? Take the code polynomial. Multiply it by the ...
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1answer
41 views

In block codes (channel coding), in practice how is the message length ($k$) fixed?

In block codes (channel coding), in practice, how is the message length ($k$) fixed? If $k$ is large, the practical implementation of it requires huge memory if look up table approach is adopted. ...
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619 views

Is there any formula for coding gain of Turbo code?

I want to compare throughput under different MCS( modulation and coding scheme). We know Shannon capacity $C = B \log(1+SNR)$ can be used to calculate throughput by SNR. However, there is no MCS ...
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45 views

Block code error control with $d \ge c+u+1$

This is about error control coding formula $$ d \ge c+u+1$$ of a block code, with $c$ being the number of correctable errors, $u$ being the number of uncorrectable errors, and $d$ being the ...
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2answers
664 views

Why does FEC seem to make BER worse at low Eb/N0?

I've been plotting BER curves and am wondering why FEC seems to make a BER curve worse at low Eb/N0 than the un-coded theoretical BER curve? My example plot below is for Differential BPSK using a ...
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1answer
94 views

Generate Minimum distance codes

I am trying to generate a set of linear block codewords of length n and have minimum hamming distance dmin. I understand Hamming codes but they are not flexible with n. One possible way I can think of ...
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739 views

Transmission capacity in “duobinary coding”

In "duo-binary signalling" how exactly is the transmission capacity increased? Because , when we encode the binary bits, the bit duration remains the same, but the amplitude will change. Then how can ...
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341 views

Important differences between BCJR and SOVA algorithms?

BCJR algorithm needs noise variance for Gamma (branch metrices) calculation. So I am wondering does SOVA (soft output Viterbi algorithm) needs noise variance?
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Can we break the Shannon capacity?

I have a friend working in wireless communications research. He told me that we can transmit more than one symbol in a given slot using one frequency (of course we can decode them at the receiver). ...
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81 views

Can we break the Shannon capacity? [duplicate]

I have a friend working in wireless communications research. He told me that we can transmit more than one symbol in a given slot using one frequency (of course we can decode them at the receiver). ...
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2answers
1k views

Meaning of channel capacity in the AWGN channel

I understand the concept of channel capacity as the maximal rate of the channel code I can apply without making a mistake in the receiver, in that sense the capacity is between 0 and 1. What I don't ...
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1answer
613 views

Limitations of Arithmetic coding?

I have been working on an assignment for university in which I have to compress an 80K message consisting of only two symbols, 'a' and 'b', having probability values of 0.6 and 0.4. I have ...
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1answer
144 views

Does any error correction code still work in such situation?

I'm looking for a kind of error correction code or solution that can correct my codeword in this case: My message holds $k$ bits, and $2k$ bits codeword (rate is $1/2$) is produced by the generator ...
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2answers
794 views

Why is a precoder necessary for DQPSK and what does it accomplish?

I've implemented a soft-decoder for DQPSK using the wonderful answers I received here: How to soft decode DQPSK? To get the soft-decoder working properly I needed to precode the data I was sending ...
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2answers
346 views

Viterbi Decoder - Symbol Alignment

With a 1/2-rate convolutional encoder, $n$ bits are encoded into $2n$ symbols. Assume we have a long encoded stream such as $[... s_0, s_1, s_2, s_3, s_4, s_5, s_6, s_7, s_8, s_9, ..., s_{100}, ...]$...
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379 views

Viterbi Decoder - How does inverting the input bits affect the result?

Does converting zeros into ones and ones into zeros in the input stream affect the decoding result? Empirically I have seen that it does not affect, decoding $[0 1 0 1 \ldots]$ and $[1 0 1 0 \ldots]$ ...
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How to soft decode DQPSK?

I'm successfully soft-decoding D-BPSK by taking the dot-product of the constellation-position of the symbol and of the previous symbol. If the result is >= 1, then the symbol phase hasn't changed and ...
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3answers
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Why is an interleaver often placed between an outer block code and an inner convolution code?

It seems that when doing FEC with a concatenated-code, an interleaver is often placed between the outer block code and the inner convolution code. The explanations I've seen say that this is because ...
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1answer
349 views

Viterbi Decoder - Decoding Continuously Encoded Stream Partially

I am in trouble with Viterbi decoder for a while. I have some questions. I need to decode messages from a continuous stream which is encoded without resetting the state metrics. Each message starts ...
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828 views

Optimal DC-free line encoding

I have a block of n bits that I'd like to encode into m bits that have an equal number of zeros and ones. I looked at protocols like 8b/10b but it wastes 25% of the data to achieve balance. As an ...
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1answer
233 views

Viterbi decoder on a bit stream where the preamble is also coded

I hope this is not off-topic for this site. In my problem, Viterbi decoder is used for decoding convolutional-coded (rate = 1/2, constraint length = 7) messages. A message is 250 bits where the ...
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1answer
2k views

increase of encoding rate increases bandwidth?

I came across this paragraph in an article about signal processing. Addition of redundant bits for improving the error probability leads to bandwidth expansion of the transmitted signal by an amount ...
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537 views

determining FEC or parity bits from percent error

I am very new to signal processing and my background is in physics. I would like to know if it is possible to determine the number of parity bits needs to theoretically get 100% transmission from a ...
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1answer
2k views

Hamming code exercise

I'm preparing for my exams I stumbled across this exercise. Now I can't seem to figure it out. Anybody can help me ? The exercise: For the 8bit data word: 00111001 the check bits are: 0111. Now if ...
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32k views

Calculate symbol rate for QAM modulation

Not sure if this is the right place to ask, feel free to move it if any other site suits this better. Anyway I am referring to QAM modulation used in US Cable TV. I know it comes under Annex B which ...
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358 views

Why is privacy scrambling a standalone block in a communications transmitter?

In some telecommunication systems, scrambling of transmitted data is applied to provide some level of security. For example, the communication system might look like: Data -> Scrambling -> ...