 You decide to use a block coder. You get to detect and correct errors at the receiver side. You pay the price of requiring more bandwidth to send the same amount of information. 6.5 Conclusion Another chapter come and gone. We learned about some interesting devices called block coders. They add extra bits to the bit stream, and that costs you bandwidth, but they give you the power to detect and correct errors at the receiver side. You saw three ways to implement this. First and simplest was the single parity check bit coder, which added one bit to each block of k bits, putting out k+1 bits. With this added bit, which made sure your k+1 bits added to 0, you could detect an odd number of errors. Rectangular coders did one better. By mapping M.N bits to (M+1).(N+1) bits, you were able to correct one bit error. Then linear block coders were introduced. They required that your output codewords be a subspace, and by making that simple requirement they gave you a powerful way to build the block coder. The block decoder uses a syndrome in order to correct errors. Finally, we gave you a way to compare block coders, by providing two perfor- mance measures and telling you how to compute them for the different block coders available to you. The end, for now. Chapter Six Problems 1. Consider a rate 6/7 channel coder using a single parity check bit. (a) What is the output for input 100101110011? (b) Does the channel decoder detect errors if (1) bit 2 is in error? (2) bit 2 and bit 8 are in error? (3) bit 2 and bit 4 are in error? (Explain.) 2. Consider a rate 9/16 rectangular code. (a) What does the channel coder output for input bits 100110001? (b) If an error occurs at bit 3, explain how the error is corrected. (c) If an error occurs at bit 3 and at bit 7, explain if and how an error is corrected. 3. (a) What are the two rules that a block code must follow in order to be a linear block code? (b) Using these two rules, make up a (4,2) linear block code, drawing a table to describe it. (c) Verify that the (4,2) code you made 