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Investigating Error Detection using CRC EE800 Project Presentation V ISHESH 11089943

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Introduction CRC generation is mostly implemented using Linear feedback shift Registers using Flip- Flops and XOR gates. But not many understand how to implement a customized parallel CRC circuit described by an arbitrary CRC generator polynomial. In this paper importance of parallel architecture is discussed and how it can be incorporated in different styles so as to compare the number of logic cells used for each Architecture.

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Serial CRC Implementation USB CRC5 implementation as LFSR using generator polynomial G(x)=x5+x2+1 The problem is that in many cases shift register implementation is suboptimal. It only allows the calculation of one bit every clock. If a design has 16-bit wide data path, meaning that every clock CRC module has to calculate CRC on 16-bit of data, this scheme will not work.

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M-Bit CRC next state Parallel CRC Generator N-Bit Data input M-Bit CRC Output Parallel CRC Generator EXAMPLE OF USB CRC5 with N=4, M=5 @ [1],[2],[5] Every clock N bits are processed.

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Mout[0] = Min[1] ^ Min [4] ^ Nin[0] ^ Nin [3] Mout [1] = Min [2] ^ Nin [1] Mout [2] = Min [1] ^ Min [3] ^ Min [4] ^ Nin [0] ^ Nin [2] ^ Nin [3] Mout [3] = Min [2] ^ Min [4] ^ Nin [1] ^ Nin [3] Mout [4] = Min [0] ^ Min [3] ^ Nin [2] Mout is the parallel CRC implementation. Mout[0] = Min[1] ^ Min [4] ^ Nin[0] ^ Nin [3] Mout [1] = Min [2] ^ Nin [1] Mout [2] = Min [1] ^ Min [3] ^ Min [4] ^ Nin [0] ^ Nin [2] ^ Nin [3] Mout [3] = Min [2] ^ Min [4] ^ Nin [1] ^ Nin [3] Mout [4] = Min [0] ^ Min [3] ^ Nin [2] Mout is the parallel CRC implementation. USB CRC5 with N=4 the parallel CRC equations

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DATA(7:0) ERRORNO ERROR DATA(7:0)* CRC #1

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ERRORNO ERROR DATA(7:0) CRC CRC* DATA(7:0)* #2

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ERRORNO ERROR DATA(7:0) CRC CRC* CRC DATA(7:0)* #3

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ERROR ‘1’ NO ERROR 0X1F 0x8041 0X8261 0X8041 0XEF Example based for #3

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FPGAData Width AlgorithmLogic Cells Registers LUT Stratix EP10S1F672C6 16CRC-16-USB8632 54 Stratix EP10S1F672C6 8CRC-16-USB2216 6 Stratix EP10S1F672C6 8CRC-16-USB810 Results Parallel/LUT CRC Generation Block

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DATA(7:0) ERRORNO ERROR DATA(7:0)* CRC ERRORNO ERROR DATA(7:0) CRC CRC* CRC DATA(7:0)* Comparison

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References [1] G. Campobello, G Patane, M Russo, “Parallel CRC Realization” (http://ai.unime.it/~gp/publications/full/tccrc.pdf) [2] G.Albertango and R. Sisto, “Parallel CRC Generation”, IEEE Micro, Vol. 10, No. 5, October 1990, pp. 63-71. [3] A. Perez, “Byte-wise CRC Calculations”, IEEE Micro, Vol. 3, No. 3, June 1983, pp. 40-50 [4] Adrian Simionescu, Nobug Consulting http://space.ednchina.com/upload/2008/8/27/5300b83c-43ea-459b-ad5c-4dc377310024.pdf [5]Evgeni Stavinov, 2010 issue of Circuit Cellar magazine, Page 40. [6] R. J. Glaise, “A two-step computation of cyclic redundancy code CRC-32 for ATM networks”, IBM Journal of Research and Development Volume 41, Issue 6 (November 1997) pp 705 - 710

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