Minimum distance decoder

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Consider a simple even parity encoder given below. Check out this ebook : Simulation of digital communication systems using Matlab. Case 1 : Assume that our communication model consists of a parity encoder, communication channel attenuates the data randomly and a hard decision decoder. The hard decision decoder makes a decision based on the threshold voltage. In our case the threshold voltage is chosen as 0.

The decoder compares the output of the hard decision block with the all possible codewords and computes the minimum Hamming distance for each case as illustrated in the table below.

For the same encoder and channel combination lets see the effect of replacing the hard decision block with a soft decision block. Voltage levels of the received signal at each sampling instant are shown in the figure. The soft decision block calculates the Euclidean distance between the received signal and the all possible codewords.

The decoder selects this codeword as the output.

Introduction of Hamming Code

Even though the parity encoder cannot correct errors, the soft decision scheme helped in recovering the data in this case. This fact delineates the improvement that will be seen when this soft decision scheme is used in combination with forward error correcting FEC schemes like convolution codesLDPC etc.

From this illustration we can understand that the soft decision decoders uses all of the information voltage levels in this case in the process of decision making whereas the hard decision decoders does not fully utilize the information available in the received signal evident from calculating Hamming distance just by comparing the signal level with the threshold whereby neglecting the actual voltage levels.

Note: This is just to illustrate the concept of Soft decision and Hard decision decoding.

minimum distance decoder

Prudent souls will be quick enough to find that the parity code example will fail for other voltage levels e. This is because the parity encoders are not capable of correcting errors but are capable of detecting single bit errors. The usage of Soft decision decoding scheme will improve the performance of the receiver by approx 2 dB when compared to hard decision scheme. Soft decision decoding scheme is often realized using Viterbi decoders.

Such decoders utilize Soft Output Viterbi Algorithm SOVA which takes into account the priori probabilities of the input symbols producing a soft output indicating the reliability of the decision. The simulation code for the mentioned special topic is not available in the ebook. It does not matter which type of decoding you use haard or soft.

Noise is noise. What can I do to get right result?Menu Menu. Search Everywhere Threads This forum This thread. Search titles only.

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Question of the Week: What should people look for when upgrading their monitor s at home? Click here to ask away! Sidebar Sidebar. JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding. Previous Next Sort by votes. Feb 15, 2 0 4, 0. Satelite Dish positioning distance relative to decoder. Sep 14, 60 0 10, Depends on the quality of the RG6 coax you are using.

Use quad shield coax for best results and look for a good brand. As for the distance it all depends on how you run your cable. Without an amplifier then anywhere between m depending on the installation and cable used. You must log in or register to reply here. What is the maximum transmission rate of coaxial cable?

Best throw distance for projector?By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Then my question is:. Is it known for what binary input channels a minimum distance decoder is equivalent to a maximum likelihood decoder? I doubt that there is a useful general characterization.

One starts assuming that the intra-symbols errors and independent, and hence. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. When is a minimum distance decoder also a maximum likelihood decoder? Ask Question. Asked 6 years, 1 month ago. Active 2 years, 1 month ago. Viewed times. Then my question is: Is it known for what binary input channels a minimum distance decoder is equivalent to a maximum likelihood decoder?

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Euclean Euclean 8 8 silver badges 22 22 bronze badges. Active Oldest Votes. Probably it is quite hard to say anything more general, and from the point of view of channel theory it might not shed any more light Alex Vong 1, 9 9 silver badges 20 20 bronze badges.

Raihan Akash Raihan Akash 1. Can you elaborate a little bit more on your argument?In coding theorygeneralized minimum-distance GMD decoding provides an efficient algorithm for decoding concatenated codeswhich is based on using an errors -and- erasures decoder for the outer code. A naive decoding algorithm for concatenated codes can not be an optimal way of decoding because it does not take into account the information that maximum likelihood decoding MLD gives.

In other words, in the naive algorithm, inner received codewords are treated the same regardless of the difference between their hamming distances. Intuitively, the outer decoder should place higher confidence in symbols whose inner encodings are close to the received word. David Forney in devised a better algorithm called generalized minimum distance GMD decoding which makes use of those information better.

minimum distance decoder

This method is achieved by measuring confidence of each received codeword, and erasing symbols whose confidence is below a desired value. And GMD decoding algorithm was one of the first examples of soft-decision decoders.

We will present three versions of the GMD decoding algorithm. The first two will be randomized algorithms while the last one will be a deterministic algorithm. The following is the algorithm description for the general case. Theorem 1.

The lemma above says that in expectation, this is indeed the case. Note that this is not enough to prove Theorem 1but can be crucial in developing future variations of the algorithm. Proof of lemma 1. Further, by the linearity of expectation, we get. In this case, E [ X i?

Decoding methods

This idea follows the algorithm below. For the proof of Lemma 1we only use the randomness to show that. This gives the deterministic algorithm below.

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Views Read Edit View history. Languages Add links. By using this site, you agree to the Terms of Use and Privacy Policy.In this dissertation we develop novel coding theoretic approaches for two problems relevant to modern communication systems.

In the first part we address the issue of reliable communication under varying sampling rate, while in the second part we focus on the analytic understanding of the performance of low density parity check LDPC codes in the low bit error rate BER region. The underlying theme in both of these somewhat non-standard yet relevant problems is that the notion of a fundamental performance metric, typically taken to be the minimum distance of an additive error correcting code, needs to be rethought when the standard assumptions on the communication no longer hold.

We first investigate the problem of overcoming inadequate timing recovery from a coding theoretic perspective. We show how to systematically thin first order Reed-Muller codes, as a representative example of highly structured additive error correcting codes with good minimum distance properties, such that the resulting thinned code is immune to additive errors and a synchronization error. The method heavily relies on the novel run-length properties also developed here.

We also propose and study number theoretic constructions of sets of strings immune to multiple repetitions, also shown to have good cardinalities. These constructions are used to develop a prefixing-based method to improve the immunity of an arbitrary code to repetition errors.

This judiciously chosen prefix carries asymptotically negligible redundancy. We also provide a low complexity message passing decoding algorithm that can handle both repetitions and additive errors.

Due to the prior limited analytical tools available to address and guarantee their performance in this regime, deployment of these powerful codes has still not met the original promise. In order to gain a better understanding of the low BER performance of LDPC codes, we introduce the notion of a combinatorial object that we call an absorbing set.

minimum distance decoder

This object is viewed as a stable point of the bit-flipping algorithm, an algorithm that can be viewed as an asymptotic 1-bit approximation to many message passing decoding algorithms. Since absorbing sets are fixed points of the message passing algorithms, the decoder can get stuck in an absorbing set that is not a codeword. In particular, if there are absorbing sets smaller that the minimum distance of the code, the decoder is likely to converge to these objects. As a result, under iterative decoding, the low BER performance will be dominated by the number and the size of dominant absorbing sets, rather that the number of minimum distance codewords and the minimum distance itself, which is considered to be the performance metric under the maximum likelihood decoding and the key property of a code.

As a case study, we analyze the minimal absorbing sets of high-rate array-based LDPC codes. We provide a comprehensive analytic description of the minimal absorbing sets for this family of codes. In this study, we demonstrate the existence of absorbing sets whose weight is strictly smaller than the minimum distance of the code.

These minimal absorbing sets, rather than minimum distance codewords, are also experimentally verified to dominate the low BER performance, further confirming the importance of our theoretical contributions.

Dish/Receiver Maximum Distance

Skip to main content.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.

It only takes a minute to sign up. Can such hypothetical decoders exist? If not, then for what fraction of error vectors beyond half min distance does the decoder always fail?

This event is called a decoder error. The occurrence of such an event is not something that the decoder can detect, and the wrong codeword is thus sent on to its destination. Variations of decoders such as list decoders that produce a list of most likely transmitted codewords can be used in such cases, but these are not called bounded-distance decoders in the sense described above.

Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Precise Failure property of Half-minimum distance decoder Ask Question. Asked 6 years, 4 months ago. Active 6 years, 4 months ago.

Viewed 52 times. There are a few decoders you could mean here, and I'm not sure which you're talking about. Nov 29 '13 at Otherwise, fail. Why would you want to guarantee a failure? Or did I misunderstand what you are asking about? Active Oldest Votes. Dilip Sarwate Dilip Sarwate 21k 1 1 gold badge 34 34 silver badges 90 90 bronze badges.

Is your decoder poly time? Is there a reference for your decoder.

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Thankyou for the help. Dec 1 '13 at Can one design a true polynomial time bounded distance decoder for this case? Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. The Overflow Blog.Forums Search forums. What's new Unread posts Latest posts New profile posts.

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Hard and Soft decision decoding

Search Advanced search…. Everywhere Threads This forum This thread. Search Advanced…. Search forums. Thread starter hikersc Start date Jan 4, JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.

Status Not open for further replies. Dec 26, 11 0. I feel sure that has been asked before but was not able to find on a search. I have upgraded to HD and the install is planned for early next week.

My question is what is the maximum distance allowed from the Dish to the Receiver without amplification. The Dish install manual mentions runs that "far exceed feet feet or more " but did not specify an upper limit the installers may use. The deal is that I have lots of tree close to my house but an unobstructed view from the lower part of my lot which would probably be about feet after burial and routing to the receivers.

minimum distance decoder

Any help here would be greatly appreciated. Dec 12, 11, 1, Dorchester, TX. There is no set distance only recommendations. Solid copper RG-6 should be used in most cases but if there is too much signal loss RG can be used in place of the RG How deep are your pockets?

I assume they will be using RG6. I have found information indicating that the distance is anywhere from to feet without a significant signal loss to require amplification. If so, will DirecTV run that much cable I need four outputs?

Anything beyond that and you will probably have to pay for the extra cable. You will also have to pay if you want the cable as extra cable. The question is why you think you need that much cable? The only time I exceeded the limit my company had not counting pole and concrete installs was when I had to wrap a townhouse and then go to the second floor.

Thanks for the comments. This will be very helpful when the installer shows up. The reason for needing about feet of cable is as follows. I pre-scouted a couple of locations based on pointing information and my tree situation. The only options I could find was placing the dish close to but in front of my house and shooting over the house. This will barely clear the trees in the middle of the lot behind my house and I am not sure that it will meet the 20 degree width needed to catch all the satellites.

As a side note, my wife does not like the idea of the dish in front of the house. My other option was the lower part of my lot where the trees end and there is a clear line-of-sight with no present or future obstructions.


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